Name:__________________________________________________Date:____________________________ Kinematics Review (Honors. Physics) Complete the following on a separate sheet of paper to be turned in on the day of the test. ALL WORK MUST BE SHOWN TO RECEIVE CREDIT. 1. The graph below describes the motion of a fly that starts out going right. 15.0 E V(m/s) 10.0 D F 5.0 5 10 15 G 20 J time (s) C H I -5.0 A -10.0 B -15.0 a. Identify section(s) where the fly moves with constant velocity going left. b. Identify section(s) where the fly moves right slowing down. c. Identify section(s) where the fly moves left speeding up. d. When is the fly at rest? e. What is the average velocity of the fly between 0 and 11 seconds? f. What is the average speed of the fly in the same time interval? g. What is the average acceleration of the fly in this time interval? h. What is the total displacement of the fly from 0 to 22 seconds? i. Identify the times when the fly changes direction. j. Draw an acceleration vs. time graph for the fly in the graph below. 15.0 a 10.0 (m/s2) 5.0 5 10 15 20 time (s) -5.0 -10.0 -15.0

2. Little Joey plays with his remote control car, and generates the motion graph below. The car starts by moving east. 15.0 x (m) 10.0 A B 5.0 5 10 15 20 Time (s) -5.0 C E F G -10.0 D -15.0 a. Identify section(s) where the car moves with constant velocity. b. Identify section(s) where the car moves west. c. Identify section(s) where the car speeds up. d. When is the car at rest? e. What is the average velocity of the car between 0 and 15 seconds? f. What is the average speed of the car in the same time interval? g. What is the total displacement of the car from 0 to 22 seconds? h. Describe the motion of the car in the sections F and G taken together. i. Draw a velocity vs. time graph describing the motion of the car from 0-20s. (An approximate shape is acceptable from 15-20s) 15.0 10.0 V(m/s) 5.0 5 10 15 20 time(s) -5.0 -10.0 -15.0 3. An architect is designing a modern airport. The largest passenger jet utilizing this airport in the future is expected to have a maximum acceleration of 3.2 m/s2, and a minimum takeoff speed of 165 km/hr. What is the minimum runway length for safe takeoff?

4. A car stopped at a red light starts moving when the light turns green and accelerates at the rate of 2.7 m/s2 for 15 seconds. The driver continues at this speed for two minutes, until he sees the next traffic signal turning red 191 m away. He reacts after 2 seconds and slams on his brakes.

a. What is the car’s acceleration if he stops just as he reaches the light? b. What is the total distance covered by the car?

c. Sketch v vs t and x vs t graphs for this motion below.

V x t t 5. A police officer, waiting for the light to change at an intersection observes a car with no licence plates in the lane next to him. The light changes and the car moves forward with an acceleration of 3.0 m/s2. Two seconds later the officer takes off in hot pursuit with an acceleration of 3.5 m/s2. After what time will the officer catch the other car? 6. James leaves his home town traveling at 70 miles per hour. An hour later Paul leaves home traveling at 75 miles per hour. The two live 580 miles apart. How long since Paul left his home will it be before they pass each other on the highway? How far away from James’ hometown are they when they pass each other? 7. a. A car starts from rest and accelerates uniformly to a speed of 15 m/s. It takes 4 seconds to reach this speed. This is part 1 of the problem. Write your givens for this part and give each variable a subscript of 1. b. The same car then hits the brakes and uniformly slows to a stop with an acceleration of -5 m/s2. This is part 2 of the problem. Write your givens for this part and give each variable a subscript of 2. (Hint: Remember the final velocity for part 1 is the initial velocity for part 2.) c. Use kinematic equations and your givens to determine the total displacement of the car. d. Draw a motion map that represents the motion of the car. Label the velocity at each second. e. Sketch the shape of the x vs. t, v vs. t, and a vs. t graphs for the motion of the car. f. Draw a numerically correct v vs. t graph. g. Use the graph to determine the total displacement traveled by the car. h. Is this the same as the car’s total distance traveled?

Answers: 1. a. E, remember the fly starts out to the right, so negative is right on this graph

b. C, I c. D d. G, J e. 0 f. 8.2 m/s g. 0.91m/s2 h. 12.5m left i. 6s, 18s j. 15 10 5 a 5 10 15 20 t -5 -10 -15

2. a. A, B, C, E b. B, C, F c. G d. D e. 0.33 m/s f. 3 m/s g. -4m h. Backwards, slowing down to a stop and then forward speeding up i. 15 v 10 5 5 10 15 20 t -5 -10 -15

3. 327.8 m x

4. -7.5 m/s2, 5354.8m v t t

5. 24.9 s

6. 3.52 hrs, 316 miles

7. See last page of this document for solutions to a-c. d. 0 e. 0 f. 0

Hints and Solutions to some problems: #1: 1e: avg velocity = displacement / time... find the area under the curve for each triangle and rectangle between 0 and 11 seconds to find the total displacement, then divide that total by the time 1f: avg speed = total distance / time... take the displacements you found in part e and make any negative displacements positive because distance is always positive. Add the distances to get the total distance, then divide that total by the time. 1g: avg acceleration = change in velocity / time OR (final velocity - initial velocity) / time 1h: continue to find the area under the curve for each triangle and rectangle then add them all #5: speeder police vi = 0 vi = 0 a = 3 a = 3.5 t+2s t Δx = vi t +1/2 a t^2 Δx = vi t +1/2 a t^2 Δx = 0 + 1/2 (3) (t+2)^2 Δx = 0 + 1/2 (3.5) t^2 set the equations equal 1/2 (3) (t+2)^2 = 1/2 (3.5) t^2 1.5 (t+2) (t+2) = 1.75 t^2

1.5( t^2 +4t+4) = 1.75 t^2 1.5 t^2 +6t +6=1.75 t^2

-0.25t^2 +6t+6 = 0 Use the quadratic formula...

#6: James Paul t+1 t v=70 v= 75 d1 d2 d1 = 70(t+1) d2 = (75)t d1 + d2 = 580

#7