A.P. Physics 1 LCHS A. Rice Unit 1 Displacement, Velocity, & Acceleration: Motion in 1 Dimension In-Class Example Problems and Lecture Notes 1. Freddy the cat started at the 3 meter position. He then walked 2 meters to the right took a nap, after waking up he walked 5 more meters to the right, he saw a bird and turned around, chasing the bird for 1 meter, finally after a long day out he continued walking west to his home 8 meters away. What was Freddy s total distance? What was Freddy s total displacement? Is Freddy s total displacement equal in size to Freddy s total distance traveled? Speed and Velocity 2. If a certain cheetah can run at a speed of 90km/h, how much time is required for it to run 400 meters at this speed? 3. Two trains are both traveling to the east on parallel tracks, where train A is initially 20 km behind train B. If train A is moving at 60km/h, and train B is moving at 50km/h, how long will it take for train A to catch up to train B?
Acceleration 4. A certain bicycle is initially moving at 5km/h, when it begins slowing over the course of 25 seconds. What is the magnitude of the bicycle s acceleration during its stopping process? 5. A car is moving in the negative direction at a velocity of -9m/s. It then undergoes a positive acceleration of +0.4m/s 2 for 10 seconds. What is the car s velocity at the end of the acceleration? 6. What are the directions of velocity and acceleration for the following objects? (Assume standard positive/negative directions for left and right.) a. Object is moving to the right and slowing down. b. Object is speeding up while moving left. Kinematic Equations
7. A car enters the freeway going 6.4 m/s and accelerates at a rate of 4.0 m/s 2 over 25 meters. What velocity does the car reach? (15.5m/s) 8. A driver going 90 km/h suddenly sees the lights of a barrier 40.0 m ahead. It takes the driver 0.75 s before he applies the brakes and the average acceleration during braking is -10.0 m/s 2. a. Does the car hit the barrier? (yes) b. How fast could the car be moving and not hit the barrier? (22m/s) 9. A certain arrow is accelerated by a bowstring at a rate of 42m/s 2. Assuming it starts from rest, how much time is required for the arrow to travel through the first 15cm displacement during its acceleration? (.085 or.09 sec) Relationships between Motion Quantities: 10. A blue marble and a red marble are both released at the same time from the top of a ramp. Both marbles roll down the ramp, accelerating at identical constant rates. After 1 second of rolling, the blue marble s displacement (x blue) and instantaneous speed (v blue) are measured. But the red marble s displacement (x red) and instantaneous speed (v red) aren t measured until it has been allowed to roll for 2 seconds. a. How does v red compare to v blue? How can you tell for sure? b. How does x red compare to x blue? How can you tell for sure? 11. In trial 1 of an experiment, an object is accelerated from rest at a constant rate for some amount of time, causing the object to move through a displacement of 25 cm. The object is stopped, and a second identical trial is performed, except the object is accelerated for four times as much time as the first trial. How far does the object move in this second trial? 12. A toy train is released to roll down an inclined track at a constant acceleration rate a, and it is moving at 3.0 m/s as it reaches the end of the track after rolling for an amount of time t. Then the train is placed on a new inclined track that is longer and angled more steeply than the first track, so on this new track the train accelerates at a rate of 2a and rolls for time 2t. What is the train s speed as it reaches the end of the new track?
Free-Fall and Vertical acceleration: 13. A cargo plane flies horizontally at a speed of 140 m/s at a height of 50 m above the ground. A supply package is dropped out of the bottom of the plane at time t=0. Two seconds later, a second package is dropped out of the bottom of the plane. Air resistance is negligible. What happens to the separation between the packages as they fall through the air? (A) The separation between packages decreases. (B) The separation between packages increases. (C) The separation between packages remains the same. (D) Cannot answer without knowing the mass of the packages. 14. A rock on Earth is dropped. What is the rock s displacement after 1 second? 15. A tennis ball is thrown straight up with an initial speed of 22.5 m/s. It is caught at the same distance above ground. a) How high does the ball rise? b) How long does it take the ball to reach its highest point? c) How long does the ball remain in the air? d) How fast was it going just before it is caught? e) What is the velocity and acceleration of the ball at the highest point?
16. Students in an experiment wish to determine the unknown constant acceleration a, that is occurring for a ball rolling down a long incline. Measurements are taken at several points along the ball s motion down the incline, for the ball s position along the incline (measured relative to its starting position) and also its rolling time (relative to the time it started rolling). Data from the experiment is shown below. Position (m) Time (s) 0 0 0.5 0.6 1.2 0.9 3.4 1.5 6.0 2.1 (a) What quantities should be graphed so that a best-fit straight line accurately fits the data points? (b) Fill in one or both of the blank columns in the above table with calculated values of your quantities, including units. (c) On the given axes, plot your data and draw a best-fit straight line. Label the axes and indicate the scale. (d) Calculate the slope of your best-fit line, then use it to help you calculate the numerical value of the ball s constant acceleration a.