1. A ball is thrown upward with an initial velocity of 20 m/s. How long will the ball take to reach its maximum height?

(A) 19.6 s
(B) 9.8 s
(C) 6.3
(D) 2.04 s

2. An airplane lands on a runway with a velocity of 150 m/s. How far will it travel until it stops if its rate of deceleration is constant at −3 m/s²?

(A) 525 m
(B) 3,750 m
(C) 6,235 m
(D) 9,813 m

3. A ball is thrown downward from the top of a roof with a speed of 25 m/s. After 2 s, its velocity will be

(A) 19.6 m/s
(B) −5.4 m/s
(C) −44.6 m/s
(D) 44.6 m/s

4. A rocket is propelled upward with an acceleration of 25 m/s² for 5 s. After that time, the engine is shut off, and the rocket continues to move upward. The maximum height, in meters, that the rocket will reach is

(A) 900
(B) 1,000
(C) 1,100
(D) 1,200

5. The total distance traveled by the object during the indicated 14 s is

(A) 7.5 m
(B) 25 m
(C) 62.5 m
(D) 77.5 m

6. The total displacement of the object during the 14 s indicated is

(A) 7.5 m
(B) 25 m
(C) 62.5 m
(D) 77.5 m

7. The average velocity over the whole time, in meters per second, of the object is

(A) 0
(B) 0.5
(C) 2.5
(D) 4.5

8. What is the total change in velocity for the object whose acceleration versus time graph is given below?

9. An object has an initial velocity of 15 m/s. How long must it accelerate at a constant rate of 3 m/s² before its average velocity is equal to twice its initial velocity?

(A) 5 s
(B) 10 s
(C) 15 s
(D) 20 s

10. A projectile is launched at an angle of 45° with a velocity of 250 m/s. If air resistance is neglected, the magnitude of the horizontal velocity of the projectile at the time it reaches maximum altitude is equal to

(A) 0 m/s
(B) 175 m/s
(C) 200 m/s
(D) 250 m/s

11. A projectile is launched horizontally with a velocity of 25 m/s from the top of a 75-m height. How many seconds will the projectile take to reach the bottom?

(A) 15.5
(B) 9.75
(C) 6.31
(D) 3.91

12. At a launch angle of 45°, the range of a launched projectile is given by

13. A projectile is launched at a certain angle. After 4 s, it hits the top of a building 500 m away. The height of the building is 50 m. The projectile was launched at an angle of

(A) 14°
(B) 21°
(C) 37°
(D) 76°

14. The operator of a boat wishes to cross a 5-km-wide river that is flowing to the east at 10 m/s. He wants to reach the exact point on the opposite shore 15 min after starting. With what speed and in what direction should the boat travel?

(A) 11.2 m/s at 26.6° E of N
(B) 8.66 m/s at 63.4° W of N
(C) 11.4 m/s at 60.9° W of N
(D) 8.66 m/s at 26.6° E of N

1. A particle has the acceleration versus time graph shown below:

If the particle begins its motion at t = 0, with v = 0 and x = 0, make a graph of velocity versus time.

2. A stone is dropped from a 75-m-high building. When this stone has dropped 15 m, a second stone is thrown downward with an initial velocity such that the two stones hit the ground at the same time. What was the initial velocity of the second stone?

3. A particle is moving in one dimension along the x-axis. The position of the particle is given, for any time, by the following position function:

x(t) = 3 t² + 2

(a) Evaluate the average velocity of the particle starting at t = 2 s for Δt = 1, 0.5, 0.2, 0.1, 0.01, 0.001 s.

(b) Interpret the physical meaning of your results for part (a).

4. A stone is dropped from a height h and falls the last half of its distance in 4 seconds. (a) What was the total time of fall? (b) From what height was the stone dropped?

5. If the average velocity of an object is nonzero, does this mean that the instantaneous velocity of the object can never be zero? Explain.

6. A girl standing on top of a roof throws a stone straight upward into the air with a certain speed. She then throws a similar stone directly downward with the same speed. Compare the velocities of both stones when they reach the ground.

7. Explain how it is possible for an object to have zero average velocity and still have nonzero average speed.

8. A mass attached to a string is twirled overhead in a horizontal circle of radius r every 0.3 s. The path is directly 0.5 m above the ground. When released, the mass lands 2.6 m away. What was the velocity of the mass when it was released, and what was the radius of the circular path?

9. A football quarterback throws a pass to a receiver at an angle of 25 degrees to the horizontal and at an initial velocity of 25 m/s. The receiver is initially at rest 30 m from the quarterback. The instant the ball is thrown, the receiver runs at a constant velocity to catch the pass. In what direction and at what speed should he run?

10. A car is moving in a straight line with velocity v. Raindrops are falling vertically downward with a constant terminal velocity u. At what angle does the driver think the drops are hitting the car’s windshield? Explain.