does **acceleration** When direction changes, so does **acceleration** When there is a constant **velocity**, there is no **acceleration** Review **Displacement** with Constant **Acceleration**: Note that: This **equation** does not require **acceleration**. v f + v i 2 x =t Example A racing car reaches a **speed** **of** 42 m/s. It then begins a uniform negative **acceleration**, using its parachute **and** braking system, **and** comes to rest 5.5 s later. Find the **distance** that/

the science **of** describing the **motion** **of** objects using words, diagrams, numbers, graphs **and** **equations**. Print for lab books The goal is to develop mental models which describe **and** explain the **motion** **of** real-world objects. Key words: vectors, scalars, **distance**, **displacement**, **speed**, **velocity**. By the end **of** this section you will be able to: Describe what is meant by vector **and** scalar quantities State the difference between **distance** **and** **displacement** State the difference between **speed** **and** **velocity** State that/

**motion** **of** a particle x-t graph vs **motion** **of** a particle with **acceleration** What are the **accelerations** **and** **displacements**? What are the **accelerations** **and** **displacements**? **Acceleration** vs. Time Graph The slope means NOTHING The area between the curve **and** the horizontal axis is the change in **velocity** a 10 s t -10 m/s/s Important **Acceleration** tells us how fast **velocity** changes **Velocity** tells us how fast position changes Kinematics **Equations** (**accelerated** **motion**) Falling Bodies, thrown up objects, **and**/

**speed** d = **distance** t = elapsed time The SI unit **of** **speed** is the m/s Average **speed** is always a positive number. Average **Velocity** Average **velocity** describes how fast the **displacement** is changing. The **equation** is: Average **velocity** is + or – depending on direction. where: vave = average **velocity** x = **displacement** t = elapsed time The SI unit **of** **velocity** is the m/s. Qualitative Demonstrations Demonstrate the **motion** **of** a particle that has an average **speed** **and** an average **velocity** that/

side **of** your **Motion** Exit Ticket. Exchange your paper with a partner when you’re finished. Determine the **distance** **and** **displacement** **of** their path ASSESS: Draw a shape with a **distance** **of** 10 **and** a **displacement** **of** 0 Complete the “Skate Park” challenge **Speed** starter Complete the “Skate Park” challenge **Speed** **Speed** – the rate at which an object changes its position What is your **speed** if you cover 240 miles in 4 hours? Never Fear! **Equation**/

Slope = **acceleration**! Understand straight-line **motion** with constant **acceleration** Goals for Chapter 2 Understand straight-line **motion** with constant **acceleration** Examine freely falling bodies Analyze straight-line **motion** when the **acceleration** is not constant 4 Introduction Kinematics is the study **of** **motion**. **Displacement**, **velocity** **and** **acceleration** are important physical quantities. A bungee jumper **speeds** up during the first part **of** his fall **and** then slows to a halt. **Displacement** vs. **Distance** **Displacement** (blue/

**of** **accelerated** **and** nonaccelerated **motions**. Apply kinematic **equations** to calculate **distance**, time, or **velocity** under conditions **of** constant **acceleration**. Changes in **Velocity** **Acceleration** is the rate at which **velocity** changes over time. An object **accelerates** if its **speed**, direction, or both change. **Acceleration** has direction **and** magnitude. Thus, **acceleration** is a vector quantity. **Acceleration** Changes in **Velocity**, continued Consider a train moving to the right, so that the **displacement** **and** the **velocity**/

) its final **velocity** (b) its **displacement** **Equations** **of** **Motion** Questions 2) A car travels at 25ms -1 for 7 seconds then slows to a halt in 5 seconds. Calculate (a) **distance** travelled in first 7 seconds (b) its **acceleration** during the last 5 seconds (c) the total **distance** travelled. 3) An arrow **accelerates** from rest at 300ms -2 through a **distance** **of** 0.5m. it then flies at steady **speed** 20m to/

© 2009 Pearson Education, Inc. Units **of** Chapter 2 Reference Frames **and** **Displacement** Average **Velocity** Instantaneous **Velocity** **Acceleration** **Motion** at Constant **Acceleration** Solving Problems Freely Falling Objects Copyright © 2009 Pearson Education, Inc. Units **of** Chapter 2 Variable **Acceleration**; Integral Calculus Graphical Analysis **and** Numerical Integration Copyright © 2009 Pearson Education, Inc. 2-1 Reference Frames **and** **Displacement** Any measurement **of** position, **distance**, or **speed** must be made with respect to a/

use this **equation**: The SI unit **of** **acceleration** is the m/s2. **Acceleration** in 1-D **Motion** has a sign! If the sign **of** the **velocity** **and** the sign **of** the **acceleration** is the same, the object **speeds** up. If the sign **of** the **velocity** **and** the sign **of** the **acceleration** are different, the object slows down. a = ∆v / ∆t Qualitative Demonstrations 1) Demonstrate the **motion** **of** a particle that has zero initial **velocity** **and** positive **acceleration**. 2) Demonstrate the **motion** **of** a/

no **acceleration** or vertical **motion** or pressure change **and** its usefulness is therefore limited in the study **of** large-scale pressure systems **and** rain-producing mechanisms. The method **of** using eqn. 3.6 to deduce wind **speed** from isobar spacing may be illustrated as follows: Fig. 3.2 shows a supposed distribution **of** mean-sea-level isobars drawn at 4hPa intervals **and** at different **distances** apart. The geostrphic wind **equation** 3/

represent? graphing review Assignment Please complete the following: **Distance**, **Displacement**, **Velocity** **and** **Speed** worksheet. Vector Components worksheet Page 193 # 3 **and** 4. 1.5 **Accelerated** **Motion** **Acceleration** = change in **velocity** over a specific time interval. When something **speeds** up or slows down. Formula: a = v /t Units: m/s2 1.5b) Graphing **Accelerated** **motion** **Velocity** changes, this changes the shape **of** the graph you are looking for. **Displacement** is found by the area under the v/

the **distance**, s, along the curve from a fixed reference point. **VELOCITY** IN THE n-t COORDINATE SYSTEM The **velocity** vector is always tangent to the path **of** **motion** (t-direction). The magnitude is determined by taking the time derivative **of** the path function, s(t). v = vut where v = s = ds/dt . Here v defines the magnitude **of** the **velocity** (**speed**) **and** ut defines the direction **of** the **velocity** vector. **ACCELERATION** IN/

unit **of** time **Velocity** is the **displacement** **of** an object in a unit **of** time Average **Speed**/**Velocity** **Equations** Symbols **Speed**/**Velocity** Problems 1.) A boy is coasting down a hill on a skateboard. At 1.0s he is traveling at 4.0m/s **and** at 4.0s he is traveling at 10.0m/s. What **distance** did he travel during that time period? (In all problems given in Regents Physics, assume **acceleration**/

2Eqn 4 Remember: when there is no change in direction then **displacement** **and** **distance** are the same thing so … Often times it is useful to consider these **equations** being applied separately for x- **and** y-directions d = **displacement** (d = s f – s i ) v i = initial **velocity** v f = final **velocity** a = **acceleration** t = time Eqns **of** Constant **Acceleration** **Motion** ECAM’s Eqn 1Eqn 3 Eqn 2Eqn 4 Remember that d = s/

gives © 2015 Pearson Education, Inc. Constant **Acceleration** **Equations** Combining **Equation** 2.11 with **Equation** 2.12 gives us a relationship between **displacement** **and** **velocity**: Δx in **Equation** 2.13 is the **displacement** (not the **distance**!). © 2015 Pearson Education, Inc. Constant **Acceleration** **Equations** For **motion** with constant **acceleration**: **Velocity** changes steadily: The position changes as the square **of** the time interval: We can also express the change in **velocity** in terms **of** **distance**, not time: Text: p. 43 © 2015/

released it The **distance** is twice the height The **displacement** is zero Classifications Scalars Vectors **Distance** **Displacement** **Speed** **Velocity** **Acceleration** Magnitude **of** a Force Forces Magnitude **of** a Momentum Momentum Torque **Speed** The average **speed** **of** an object is defined as the total **distance** traveled divided by the total time elapsed **Speed** is a scalar quantity **Speed**, cont Average **speed** totally ignores any variations in the object’s actual **motion** during the trip The total **distance** **and** the total/

Distinguish between linear, angular, **and** general **motion** Define **distance** traveled **and** **displacement**, **and** distinguish between the two Define average **speed** **and** average **velocity**, **and** distinguish between the two Define instantaneous **speed** **and** instantaneous **velocity** Objectives Define average **acceleration** Define instantaneous **acceleration** Name the units **of** measurement for **distance** traveled **and** **displacement**, **speed** **and** **velocity**, **and** **acceleration** Use the **equations** **of** projectile **motion** to determine the vertical or/

**of** directions **and** signs for **velocity**, **displacement**, **and** **acceleration**. Solve problems involving a free-falling body in a gravitational field. Uniform **Acceleration** in One Dimension: **Motion** is along a straight line (horizontal, vertical or slanted). Changes in **motion** result from a CONSTANT force producing uniform **acceleration**. The cause **of** **motion** will be discussed later. Here we only treat the changes. The moving object is treated as though it were a point particle. **Distance** **and** **Displacement** **Distance**/

Relative **Velocity** **and** Riverboat ProblemsRelative **Velocity** **and** Riverboat Problems 8.Independence **of** Perpendicular Components **of** MotionIndependence **of** Perpendicular Components **of** **Motion** Vectors **and** Direction All quantities can by divided into two categories - vectors **and** scalars.vectors **and** scalars A vector quantity is fully described by both magnitude **and** direction. A scalar quantity is fully described by its magnitude. Examples **of** vector include **displacement**, **velocity**, **acceleration**, **and** force. Each **of** these/

problems usually involve a car moving with an initial **velocity** toward an object a measured **distance** away. Reaction time is the time it takes for the driver to take their foot off **of** the gas pedal **and** press on the brake pedal. During the reaction time, the car does not **accelerate** **and** maintains a constant **speed**; therefore, the only **equation** you should use is Reaction Time If you/

Wesley publisher Outline The Big Idea Scalars **and** Vectors **Distance** versus **displacement** **Speed** **and** **Velocity** **Acceleration** Describing **motion** with diagrams Describing **motion** with graphs Free Fall **and** the **acceleration** **of** gravity Describing **motion** with **equations** The Big Idea Kinematics is the science **of** describing the **motion** **of** objects using words, diagrams, numbers, graphs, **and** **equations**. Kinematics is a branch **of** mechanics. The goal **of** any study **of** kinematics is to develop sophisticated mental models which/

**of** **motion** symbol = s Measurement **of** **Speed** Total **distance** : the sum **of** the all changes in position Time : an interval **of** change measured in seconds Position : Separation between the object **and** the reference point Types **of** **Speed** Rest : no change in **motion** Instantaneous: the current **speed** **of** an object at a point **of** time Average : two ways to determine the “mean” movement Total **distance** / Total time Sum **of** the individual **speeds** / number **of** **speed** measurements **Speed** is a scalar quantity **Velocity** **Displacement**/

. Thus the **displacement** **of** the object is 75 meters during the 10 seconds **of** **motion**. Example 1 1. Rennata Gas is driving through town at 25.0 m/s **and** begins to **accelerate** at a constant rate **of** –1.0 m/s2. Eventually Rennata comes to a complete stop. a. Represent Rennatas **accelerated** **motion** by sketching a **velocity**-time graph. Use the **velocity**- time graph to determine the **distance** traveled while decelerating/

a **velocity** / time graph to find **displacement** The calculation **of** the **displacement** **of** the body is the same as calculating the area under the graph between 0 **and** 8 seconds © David Hoult 2009 The area under a **velocity** / time graph represents the **displacement** **of** the body © David Hoult 2009 **Equations** **of** **Motion** © David Hoult 2009 These **equations** are useful when bodies move with uniform **acceleration**. Symbols used in the **equations**: © David Hoult 2009 These **equations** are/

/s 2 g is always directed downward toward the center **of** the earth Ignoring air resistance **and** assuming g doesn’t vary with altitude over short vertical **distances**, free fall is constantly **accelerated** **motion** Free Fall – an object dropped Initial **velocity** is zero Let up be positive Use the kinematic **equations** Generally use y instead **of** x since vertical **Acceleration** is g = -9.80 m/s 2 v o/

t seconds is (v – u) Change in **velocity** / sec. = v – u / t = a v = u + at -----(1) **Equations** **of** **Motion** Under Uniform **Acceleration** k17 2. **Equation** **of** **Motion**: (Relation between s, u, a **and** t) Let a body moving with an initial uniform **velocity** u be **accelerated** with a uniform **acceleration** a for time t. If v is the final **velocity**, the **distance** s which the body travels in time t is determined as/

is **motion** **and** how does it change? DO NOW: A skater increases his **speed** from 2.0 m/s to 10.0 m/s in 3.0 s. What is his **acceleration**? Home Work: Worksheet 2.2 17 Check Which **of** the following statements correctly define **acceleration**? A. **Acceleration** is the rate **of** change **of** **displacement** **of** an object. B. **Acceleration** is the rate **of** change **of** **velocity** **of** an object. C. **Acceleration** is the amount **of** **distance** covered/

solve for time: Section 3.2-26 Section 3.2 Section 3.2 **Motion** with Constant **Acceleration** An Alternative Expression This **equation** can be solved for the **velocity**, v f, at any time, t f. The square **of** the final **velocity** equals the sum **of** the square **of** the initial **velocity** **and** twice the product **of** the **acceleration** **and** the **displacement** since the initial time. Section 3.2-27 Section 3.2 Section 3/

a) define **displacement**, **speed**, **velocity** **and** **acceleration**. (b) use graphical methods to represent **displacement**, **speed**, **velocity** **and** **acceleration**. (c) find the **distance** traveled by calculating the area under a **velocity**-time graph. (d) use the slope **of** a **displacement**-time graph to find the **velocity**. (e) use the slope **of** a **velocity**-time graph to find the **acceleration**. Assessment Objectives: (f) derive, from the definitions **of** **velocity** **and** **acceleration**, **equations** which represent uniformly-**accelerated** **motion** in a/

.g. volume, mass, length, **speed**, time, work **and** density etc. 42 Lecture # 5 Unit 3.3 b Contents: 1.1st **Equation** **Of** Linear **Motion** For Constant Linear **Acceleration** 2.Example **of** **Equation** # 1 3.2nd **Equation** **of** Linear **Motion** for Constant Linear **Acceleration** 4.Example **Of** **Equation** # 2 5. 3rd **Equation** **of** Linear **Motion** for Constant Linear **Acceleration** 6.Example **of** **Equation** # 3 7.**Distance**, Time graph 8.**Velocity**, Time graph 43 1 st **Equation** **Of** Linear **Motion** For Constant Linear **Acceleration** If an object is/

(**speed**) d = **distance** t = elapsed time SI unit: m/s Average **speed** is always a positive number. Average **Velocity** How fast the **displacement** **of** a particle is changing. v ave = ∆x ∆t where: v ave = average **velocity** ∆x = **displacement** ∆t = change in time SI unit: m/s Average **velocity** is/**of** mile marker 0 traveling at 30.0 m/s due south. Car A is **speeding** up with an **acceleration** **of** magnitude 1.5 m/s 2, **and** car B is slowing down with an **acceleration** **of** magnitude 2.0 m/s 2. Write x-vs-t **equation** **of** **motion**/

change in position **of** an object. Average **speed** is the **distance** traveled divided by the time it took; average **velocity** is the **displacement** divided by the time. Instantaneous **velocity** is the limit as the time becomes infinitesimally short. Summary **of** Chapter 2 Average **acceleration** is the change in **velocity** divided by the time. Instantaneous **acceleration** is the limit as the time interval becomes infinitesimally small. The **equations** **of** **motion** for constant **acceleration** are given/

**velocity** in terms **of** **acceleration** **and** **displacement** Does not give any information about the time Section 2.6 When a = 0 When the **acceleration** is zero, v xf = v xi = v x x f = x i + v x t The constant **acceleration** model reduces to the constant **velocity** model. Section 2.6 Kinematic **Equations** – summary Section 2.6 Graphical Look at **Motion**: **Displacement** – Time curve The slope **of** the curve is the **velocity**/

basis associated with them. While our emphasis will often be upon the conceptual nature **of** physics, we will give considerable **and** persistent attention to its mathematical aspect. Words **and** Quantities The **motion** **of** objects can be described by words - words such as **distance**, **displacement**, **speed**, **velocity**, **and** **acceleration**. These mathematical quantities which are used to describe the **motion** **of** objects can be divided into two categories. The quantity is either a vector or/

. __________ 4. The **speed** limit sign says 45 mph. __________ Physics Daily Warmup #16 instantaneous average instantaneous 2.4 Kinematics **Equations** (Constant **Acceleration**) By combining the formulas **and** descriptions **of** **motion** we have learned so far, we can derive three basic **equations**. 1) **velocity** as a function **of** time 2) **displacement** as a function **of** time 3) **velocity** as a function **of** **displacement** Choose the **equation** that has three **of** your known variables, **and** solve for the/

**equation** : Where t is in seconds **and** the angles in the parentheses are in radians. (a)Determine the amplitude, frequency, **and** period **of** the **motion**. (b)Calculate the **velocity** **and** **acceleration** **of** the object at any time t. (c)Using the results **of** part (b), determine the position, **velocity**, **and** **acceleration** **of** the object at t = 1.00 s. (d)Determine the maximum **speed** **and** maximum **acceleration** **of** the object. (e)Find the **displacement** **of** the object between t = 0 **and**/

0 (F) 0 Section 2-5: **Motion** at Constant **Acceleration** Write the **equation** for **velocity** as a function **of** time for constant **acceleration**. Write the **equation** for average **velocity** under constant **acceleration**. Section 2-5: **Motion** at Constant **Acceleration** Write the **equation** for position as a function **of** time for constant **acceleration**. Write the **equation** that relates **velocity**, **acceleration**, **and** position (the “no time” **equation**). Section 2-5: **Motion** at Constant **Acceleration** Identify every symbol that you used in/

finding the height times the width **of** the **velocity** graph. c)This yields a result consistent with applying the **equation** for linear **motion**. d)All **of** the above are true. © 2014 Pearson Education, Inc. Which **of** the following situations corresponds to a positive **acceleration**? a)An object moving in the –x direction **and** slowing down b)An object moving in the –x direction **and** **speeding** up c)An object moving/

**Equations** **of** Kinematics for Constant **Acceleration** For one dimensional **motion** it is customary to dispense with the use **of** boldface symbols overdrawn with arrows for the **displacement**, **velocity**, **and** **acceleration** vectors. We will, however, continue to convey the directions with a plus or minus sign. 2.4 **Equations** **of** Kinematics for Constant **Acceleration** Let the object be at the origin when the clock starts. 2.4 **Equations** **of** Kinematics for Constant **Acceleration** **Equations** **of** Kinematics for Constant **Acceleration**/

menu Chapter 2 Sign Conventions for **Velocity** Section 1 **Displacement** **and** **Velocity** Copyright © by Holt, Rinehart **and** Winston. All rights reserved. ResourcesChapter menu Section 2 **Acceleration** Chapter 2 Objectives Describe **motion** in terms **of** changing **velocity**. Compare graphical representations **of** **accelerated** **and** nonaccelerated **motions**. Apply kinematic **equations** to calculate **distance**, time, or **velocity** under conditions **of** constant **acceleration**. Copyright © by Holt, Rinehart **and** Winston. All rights reserved/

total time elapsed ▫**Speed** is a scalar quantity **Speed**, cont Average **speed** totally ignores any variations in the object’s actual **motion** during the trip May be, but is not necessarily, the magnitude **of** the **velocity** The total **distance** **and** the total time are all that is important SI units are m/s ▫same units as **velocity** Other ways **of** representing the same **equation** Slope Graphical Interpretation **of** **Velocity** **Velocity** can be determined from/

using **equations** with the concepts **of** **distance**, **displacement**, **speed**, average **velocity**, instantaneous **velocity**, **and** **acceleration** 4F identify **and** describe **motion** relative to different frames **of** reference © Houghton Mifflin Harcourt Publishing Company Preview Objectives One Dimensional **Motion** **Displacement** Average **Velocity** **Velocity** **and** **Speed** Interpreting **Velocity** Graphically Chapter 2 Section 1 **Displacement** **and** **Velocity** © Houghton Mifflin Harcourt Publishing Company Section 1 **Displacement** **and** **Velocity** Chapter/

the average **velocity** in km/min **and** in km/h. –Answer: 1.2 km/min to the north or 72 km/h to the north **Motion** in One DimensionSection 1 **Speed** **Speed** does not include direction while **velocity** does. **Speed** uses **distance** rather than **displacement**. In a round trip, the average **velocity** is zero but the average **speed** is not zero. **Motion** in One DimensionSection 1 Instantaneous **Velocity** **Velocity** at a single instant **of** time/

. So why is concept **of** **velocity** so important? if **motion** is 1-D without changing direction; **speed** = magnitude **of** **velocity** because **speed** = magnitude **of** **velocity** because **distance** traveled = magnitude **of** **displacement** instantaneous **speed** = magnitude **of** instantaneous **velocity** Because **acceleration** is a vector, all **of** **equations** are vector **equations** Because **acceleration** is a vector, all **of** **equations** are vector **equations**. **Acceleration** can be in any direction to the **velocity** **and** the **motion** will depend on that. ONLY/

**velocity** in terms **of** **acceleration** **and** **displacement** Does not give any information about the time Section 2.6 When a = 0 When the **acceleration** is zero, v xf = v xi = v x x f = x i + v x t The constant **acceleration** model reduces to the constant **velocity** model. Section 2.6 Kinematic **Equations** – summary Section 2.6 Graphical Look at **Motion**: **Displacement** – Time curve The slope **of** the curve is the **velocity**/

. So why is concept **of** **velocity** so important? if **motion** is 1-D without changing direction; **speed** = magnitude **of** **velocity** because **speed** = magnitude **of** **velocity** because **distance** traveled = magnitude **of** **displacement** instantaneous **speed** = magnitude **of** instantaneous **velocity** Because **acceleration** is a vector, all **of** **equations** are vector **equations** Because **acceleration** is a vector, all **of** **equations** are vector **equations**. **Acceleration** can be in any direction to the **velocity** **and** the **motion** will depend on that. ONLY/

**Motion** Some **Motion** Terms **Distance** & **Displacement** **Velocity** & **Speed** **Acceleration** Uniform **motion** Scalar.vs. vector Scalar versus Vector Scalar - magnitude only (e.g. volume, mass, time) Vector - magnitude & direction (e.g. weight, **velocity**, **acceleration**) Pictorial Representation An arrow represents a vector – Length = magnitude **of** vector – Direction = direction **of** vector Pictorial Representation This arrow could represent a vector **of** magnitude 10 point to the “right” This arrow could represent a vector **of** /

START v 4s3s2s1s0 a x Slowing up in - direction a **and** v OPP direction 5s START v 4s3s2s1s 0 a x **Speeding** up in - direction a **and** v SAME direction 5s **Displacement** **and** **velocity** are in the direction **of** **motion** When **acceleration** is in the SAME direction as **velocity**, the object is **speeding** up When **acceleration** is in the OPPOSITE direction to **velocity**, the object is slowing down START 4s3s2s1s5s x t=5/

vertical direction, but sign will be determined by coordinate system. X-Dir : motionY-Dir : **motion** Before (1-D) & Now (2-D) 2-D **motion** Terms used to describe 2-D **motion** Position **Distance** & **Displacement** **Speed** & **Velocity** Average & Instantaneous **Acceleration** Average & Instantaneous Position **and** **Displacement** The position **of** an object is described by its position vector, The **displacement** **of** the object is defined as the change in its position. CH4 In two- or three/

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