# Speed, velocity and acceleration. Motion When an object changes its position, motion has occurred. –Distance- How far an object has moved. –Displacement-

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Speed, velocity and acceleration

Motion When an object changes its position, motion has occurred. –Distance- How far an object has moved. –Displacement- How far an object has moved in relation to its starting point. –Consider direction Example: Two runners travel along the same straight path in a straight line for 500 meters. At the end of the run their distances are the same but their displacements are different. How can this be so?

1Both Mr Rabbit and Mr Tortoise took the same round trip, but Mr Rabbit slept & returned later.

Comment on their their argument. Me, as I spent less time on the trip. No, I travelled longer distance every minute. Who runs faster?

SPEED Distance an object travels per unit of time Relationships between speed, distance, and time: Speed = Distance/ Time = d/ t »Constant Speed- speed does not change over time »Average Speed- speed of motion when speed is changing Avg Speed = Total Distance/ Total Time »Instantaneous Speed- speed at any given moment in time (speedometer)

Speed How can we describe how fast an object moves? A car on Tolo Highway travels 90 km in 1 hour. We say that the car travels at a speed of 90 km/h.

Speed Speed is a measure of how fast something moves. Speed = distance travelled per unit of time SI unit: m/s or km/h (for long distances) How can we describe how fast an object moves?

KINDS OF SPEED Average, Instantaneous, Constant

and speeds up again to 60 km/h Average speed Its average speed over the whole journey overall distance travelled total time of travel slows down to 0 km/h A car travels at 50 km/h =

Average speed does not tell the variations during the journey. On most trips, the speed at any instant is often different from the average speed.

Instantaneous speed speed at any instant The word ‘speed’ alone  instantaneous speed Instantaneous speed  distance travelled in an extremely short time interval Simulation

Speedometer tells the car’s speed at any instant! Instantaneous speed

Constant Speed Elapsed time (seconds) Distance (meters) 00 24 48 612 816 1020 1224 Not changing speed. Same amount of speed from beginning to last.

Motion Graphs – Position vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Graphing Motion Graph distance on the y- axis and time on the x-axis Slope = rise = distance = speed run time run time

Distance - Time Graph If something is not moving, a horizontal line is drawn. If something starts out slow and then speeds up, its change in speed can look like this.

Learning Checkpoint This graph shows several stages of motion: Stage 1: 100 m in 10 s Stage 2: 50 m in 10 s Stage 3: 150 m in 20 s Calculate the speed as indicated by each of the colors. Calculate the average speed. What is the total distance? What is the displacement?

Solution Stage 1: S= d/ t 100 m/ 10 s= 10 m/s Stage 2: S= d/t 50 m/ 10 s= 5 m/s Stage 3: S= d/t 150 m/ 20 s= 7.5 m/s Ave Speed= Tot d/ Tot t 300 m/ 40 s= 7.5 m/s Distance = 300 meters Displacement = 0 meters

KINDS OF VELOCITY Average, Instantaneous, Constant

Velocity rate of change of displacement. a speed in a given direction or velocity a vector quantity direction magnitude (speed) Velocity is...

speed = 300 km/h direction = west Train drivers concern speed only. Speed with direction Pilots concern velocity (direction & speed). speed = 90 km/h

Average velocity Average velocity = overall displacement total time of travel direction of velocity = direction of overall displacement

Instantaneous velocity The velocity at any instant is called instantaneous velocity. If a car moves at a constant velocity... … its average and instantaneous velocities have the same value.

Constant VELOCITY Elapsed time (seconds) Distance (meters) 00 24 48 612 816 1020 1224 Not changing speed. Same amount of speed from beginning to last.

Graph: Constant Velocity

Velocity Time Graph Elapsed time (seconds) Distance (meters) Velocit y (m/s) 00.0 24.02.0 48.02.0 612.02.0 816.02.0 1020.02.0 1224.02.0 Copy the data chart and construct a VELOCITY vs. TIME Graph

Terminal Velocity Terminal velocity- the velocity at which the upward force of air resistance equals the downward force of gravity. Once you reach this velocity you will no longer accelerate. (just stay at the same velocity) Parachutes increase your surface area to increase your air resistance in order to reduce your terminal velocity so you don’t die when you hit the ground.

Velocity Questions 1)How far does Bob run if he maintains an average velocity of 3 m/s for 10 s? 2)List three ways you can change the velocity of your car. 3)Is it possible to go around a corner without changing velocity? Explain. 4)One car is going 25 miles/hr north, another car is going 25 miles/hr south. Do they have the same velocity? Explain.

Q1The world record... ( ) Average speed = 10.49 = 9.53 m/s or 34.3 km/h 100 The world record of women 100-m race is 10.49 s. What is the average speed?

In an orienteering event, Maria and Karen reach their control points at the same time. Q2In an orienteering event... start, 10:00 am Maria, 10:30 am Karen, 10:30 am Who runs in a higher average velocity?

AMaria. BKaren. CUndetermined since their paths are unknown. DIncomparable since they run along different directions. Who runs in a higher average velocity? Q2In an orienteering event...

Note: The distance travelled is equal to magnitude of displacement only if it is a straight-line motion. Speed is usually larger than the magnitude of velocity. Q3True or false: (T/F) Average speed of an object  magnitude of its average velocity.

A man takes a walk starting from rest and ending at rest. Q4True or false: (T/F) It is possible for him to attain an average speed of 5 km h –1 but he never goes faster than 5 km h –1.

ACCELERAT ION

Acceleration measures the change in velocity Acceleration =  velocity per unit time direction speed overall change in velocity total time taken = m/s 2 Unit: m/s / s vector quantity =

Acceleration When a car moves faster and faster, its speed is increasing (velocity changed).

DEceleration When a car moves slower and slower, its speed is decreasing (- velocity changed).

When a car changes direction, its velocity changes too. Acceleration

If you have starting and ending velocity or speed, find that before you use the triangle. If not, use triangle to find change in velocity (  v), then find initial or final velocity  v = ending velocity – starting velocity Solving Acceleration Problems using Acceleration Triangle a vv t

If a car accelerates at 2 m/s, what does that mean? 3Acceleration t = 1 s v = 2 m/s,  v = 2 m/s v = 0 t = 2 s v = 4 m/s,  v = 2 m/s v = 6 m/s,  v = 2 m/s t = 3 s 1 m t = 0 3 m 5 m

Acceleration at constant speed An object moving in a circle at constant speed is always accelerating (changing direction).

Motion Graphs – Velocity vs. Time constant, rightward (+) velocity of +10 m/s a rightward (+), changing velocity - that is, a car that is moving rightward but speeding up or accelerating

Acceleration Questions 1)A dragster going at 10 m/s increases its velocity to 25 m/s in 4 seconds. What is its acceleration? 2)The driver of a car steps on the brakes, and the velocity drops from 20 m/s to 8 m/s in a time of 2 seconds. Find his acceleration. 3)Find the acceleration of a car that travels at a constant velocity of 40 Km/hr for 10 s. 4)Challenge: Calculate the velocity of a skateboarder who accelerates from rest for 4 seconds down a ramp at an acceleration of 5 m/s 2.

Uniform Acceleration : Velocity vs. Time Elapsed time (seconds) Distance (meters) 0.00 4.08 8.032 12.072 16.0128 20.0200 24.0288

What is the magnitude of the object’s total displacement after 4 seconds What is the average speed after 3 seconds? Graph Question 8m V= d/t V= 8m/3s V= 2.66 m/s

Summary Distance and time measurements can be used to describe the velocity and acceleration The Shape of the Distance vs. Time determines the type of motion – Rest : Straight line parallel to time axis – Constant Speed : Straight line on a slope (magnitude of the speed) – Constant Acceleration: Curved line The Shape of the Velocity vs. Time determines the type of motion – Rest : Straight line on the time axis – Constant Speed : Straight line parallel to the Time axis – Constant Acceleration: Straight line on a slope (magnitude of the Acceleration)

Q1A running student... A running student is slowing down in front of a teacher. With reference to the sign convention, Acceleration of student: positive / negative Velocity of student: positive / negative +ve

Quantity Unit Scalar/Vector Speed ______ _____ Velocity ______ _____ Change in velocity ______ _____ Acceleration ______ _____ Q2When time is measured... Unit of time: hour (h) km h –1 km h –2 scalar vector Unit of distance/displacement: kilometer (km)

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