Physics 1100 – Spring 2012 Chapter 3 - Linear Motion Motion is relative Speed –Instantaneous speed –Average speed Velocity Acceleration –Acceleration on Inclined planes Free Fall –How Fast –How Far –How Quickly How Fast Changes

Physics 1100 – Spring 2012 Speed and Velocity speed = distance/time (miles/h, meters/s, etc.) –instantaneous speed = speed over a very short interval –average speed = total distance traveled/total time interval =  d/  t –distance (d) = average speed x time elapsed velocity = speed + direction of motion constant speed (or velocity) means equal distances were covered in equal times

Physics 1100 – Spring 2012 Constant Velocity Motion – No Forces If no external forces are acting, velocity is constant Position changes, at a steady (constant) rate v= 1 m/s 1 m/s 1 m/s 1 m/s 1 m/s 1 m/s to right How does determination of velocity depend on choice x=0 and t=0? x =1 m 2 m 3 m 4 m 5 m 6 m 7 m t=0 sec 1 sec 2 sec 3 sec 4 sec 5 sec 6 sec

Physics 1100 – Spring 2012 A Data Table Time 0 sec Position 1 meter Velocity = dist/time & direction 1 sec2 meters1 m/s to right 2 sec3 meters1 m/s to right 3 sec4 meters1 m/s to right

Physics 1100 – Spring 2012 Speed vs. Velocity Speed is the rate of motion (how fast) Speed = distance / time The satellite has a speed of 15,000 mi/hr A car moves with a speed of 60 miles an hour Velocity is speed plus directional information: The car is moving at 1 mile/minute towards Chicago Most of this course is straight line motion and velocity and speed can be used interchangeably

Physics 1100 – Spring 2012 Discussion Questions Questions: 1.A yellow car is heading East at 100 km/h and a red car is going North at 100 km/h. ( A ) They have the same speed and velocity (B) They have the same speed and different velocities (C) They have the same velocity and different speeds (D) Both their velocity and speed are different 2.A 16-lb bowling ball in a bowling alley in Denver heads due north at 10 m/s. At the same time, a purple 8-lb ball heads due north at 10 m/s in an alley in Tacoma. Do they have the same velocity? (A) They have the same speed and velocity (B) They have the same speed and different velocities (C) They have the same velocity and different speeds (D) Both their velocity and speed are different

Physics 1100 – Spring 2012 Vectors and Scalars in Physics A quantity specified by its magnitude is called a Scalar. For example: Volume or Time A Vector has magnitude and direction. Compare “Ball is 12 meters North of the space needle” to “Ball is 10 meters from here” Which of these descriptive properties are vectors? –Position –Mass –Color –Speed –Velocity –Temperature Used interchangeably in casual language, but not in physics

Physics 1100 – Spring 2012 Galileo’s Inclined Plane

Physics 1100 – Spring 2012 Acceleration If an object’s velocity changes, it’s accelerating. The change can be in the speed of motion, in the direction of motion, or both. Acceleration is a generic term  velocity change –includes “deceleration” Can you feel if you’re moving with a constant velocity? Can you feel being accelerated? Why? Definition: acceleration (a) = change in velocity/ time interval –time rate of change, not the total change

Physics 1100 – Spring 2012 Acceleration is the rate of change of velocity A constant acceleration means that the object’s velocity is changing at a constant rate –Example: if the acceleration is along the direction of motion, the speed grows by the same amount in each time interval (e.g., second) if the speed changes by 1 meter per second each second, the acceleration is (1 meter per second) per second, or 1 m/s 2. if v = 15 m/s at time t = 0, and a = 1 m/s 2, then v = 16 m/s at t = 1 sec v = 17 m/s at t = 2 sec v = 20 m/s at t = 5 sec

Physics 1100 – Spring 2012 Acceleration is a Vector too Direction of acceleration = direction in which velocity changes –Accel. in same direction as velocity  speed increases –Accel. in direction opposite to velocity  speed decreases –Accel. at right angles to velocity  direction changes Example: An unexpected shove from the side as you run straight down a hallway might send you careening into the wall. Circular motion is produced by acceleration (gravity)

Physics 1100 – Spring 2012 Discussion Questions, cont. 1. A sprinter who is running a 200 meter race covers the second 100 meters in less time than it takes to cover the first 100 meters. Why? 2. When you let go of a ball, does it accelerate? In which direction? What about when it hits the floor? If you throw it upwards, does it accelerate then? Which direction? 3. If you are driving East and apply the brakes to stop your car, in what direction are you accelerating?

Physics 1100 – Spring 2012 Falling Bodies Galileo Inclined Plane Experiments –same amount of speed increase/unit time interval (constant a!!) –value increased as plane was tilted up –vertical = acceleration gravity (g) = 10 m/s/s = 10 m/s 2 –all objects fall at same rate! – FREE FALL v = at = gt How far does a falling object go? d = ½ (acceleration x time x time) = ½ at 2 d = ½ gt 2 Why doesn’t an object fall 10 m in 1 second? d = average velocity x time

Physics 1100 – Spring 2012 Velocity and Distance for a Falling Object

Physics 1100 – Spring 2012 Free Fall

Physics 1100 – Spring 2012 Discussion Question 1.You throw a ball into the air at a velocity of 30m/s. What is its velocity 1, 2, 3, 4, 5, and 6 seconds after you let it go? 2.What is its height at those times? 3.What is its acceleration at those times?

Physics 1100 – Spring 2012

“I shoot an arrow in the air”

Physics 1100 – Spring 2012 Summary

Physics 1100 – Spring 2012 Class Problems On planet Splat, the acceleration due to gravity is 40.0 m/s 2. What would a rock’s velocity be 3 sec after you dropped it on Splat? A) 10 m/s 2 B) 40 m/s 2 C) 80 m/s 2 D) 120 m/s 2

Physics 1100 – Spring 2012 On planet Splat, the acceleration due to gravity is 40.0 m/s 2. What would a rock’s velocity be 3 sec after you dropped it on Splat? Velocity increases by 40 m/s in each second. Starts from rest, i.e. v = 0 at t = 0 So, v(0 s) = 0 m/s, v(1 s) = 40 m/s, v(2 s) = 80 m/s, v(3 s) = 120 m/s. Class Problems

Physics 1100 – Spring 2012 Class Problems A motorist wishes to travel 40 kilometers at an average speed of 40 km/h. During the first 20 kilometers, an average speed of 40km/h is maintained. During the next 10 kilometers, however, the motorist goofs off and only averages 20 km/h. To drive the last 10 kilometers and average 40 km/h the motorist must drive: A) 60 km/h B) 90 km/h C) 80 km/h D) Faster than the speed of light

Physics 1100 – Spring 2012 A truck is moving at constant velocity. Inside the storage compartment, a rock is dropped from the midpoint of the ceiling and strikes the floor below. The rock hits the floor A) exactly below the midpoint of the ceiling. B) behind the midpoint of the ceiling. C) ahead of the midpoint of the ceiling. D) more information is needed to solve this problem. E) none of these Class Problems

Physics 1100 – Spring 2012 The two measurements necessary for calculating average speed are A) distance and acceleration. B) acceleration and time. C) velocity and time. D) distance and time. E) velocity and distance. Class Problems

Physics 1100 – Spring 2012 A hockey puck is set in motion across a frozen pond. If ice friction and air resistance are neglected, the force required to keep the puck sliding at constant velocity is: A) equal to its weight divided by its mass. B) equal to its weight. C) zero. D) equal to the product of its mass times its weight. Class Problems

Physics 1100 – Spring 2012 Twelve seconds after starting from rest, an object falling freely will have a speed of A) 100 m/s. B) 50 m/s. C) 10 m/s. D) more than 100 m/s. Class Problems

Physics 1100 – Spring 2012 A ball tossed vertically upward rises, reaches its highest point, and then falls back to its starting point. During this time the acceleration of the ball is always A) directed upward. B) opposite its velocity. C) in the direction of motion. D) directed downward. Class Problems

Physics 1100 – Spring 2012 If you drop an object, it will accelerate downward at a rate of 10 meters per second per second. If you instead throw it downwards, its acceleration (in the absence of air resistance) will be A) greater than 10 meters per second per second. B) 10 meters per second per second. C) less than 10 meters per second per second. Class Problems

Physics 1100 – Spring 2012 If a projectile is fired straight up at a speed of 10 m/s, the total time to return to its starting position is about A) 20 seconds. B) 1 second. C) 2 seconds. D) 10 seconds. E) not enough information to estimate Class Problems

Physics 1100 – Spring 2012 A ball is thrown upwards. Neglecting air resistance, what initial upward speed does the ball need to remain in the air for a total time of 10 seconds? A) about 60 m/s B) about 80 m/s C) about 100 m/s D) about 50 m/s E) about 110 m/s Class Problems