# Exercises - Acceleration, Velocity, and Speed

1. A ball is thrown vertically downward from the top of a 220 foot building with an initial velocity of -22 feet per second. Find the following:

1. the velocity of the ball after 3 seconds
2. the velocity of the ball after falling 108 feet
2. A ball rolls down a hill. At time $t$ (in seconds), its velocity is $v(t) = -12t$ (in feet per second). If the initial position of the ball is 96 feet from the bottom of the hill, find the following:

1. $s(t)$, the distance between the ball and the bottom of the hill at time $t$;
2. $a(t)$, the acceleration of the ball at time $t$; and
3. the ball's velocity when it reaches the bottom of the hill.
3. A boy who is 4 feet tall is standing on a bridge above a creek. He pitches a rock upward with a velocity of 48 ft/s. After 6 seconds the rock makes a splash in the creek.

1. Find the height (above the creek) of the bridge.
2. Find the maximum height above the top of the bridge which is reached by the rock.
4. An object is thrown upward with an initial velocity of 64 ft/s from a height of 192 ft above the ground. How long does it take for the object to reach the ground?

5. A rock is dropped from the top of a building and hits the ground in 3 seconds. Determine the height of the building.

6. A ball is thrown directly upward from a point 24 ft above the ground with an initial velocity of 40 ft/s.

1. How high will the ball rise?
2. When will the ball reach the ground?
7. A ball is thrown upward from the ground with initial velocity 24 ft/s.

1. What will be the maximum height reached?
2. How high above the ground is the ball when its velocity is -12 ft/s?
8. A rock is thrown vertically upward from the top of a cliff 100 feet above the ground with an initial velocity of 60 ft/s.

1. When will the rock reach the highest point in its path?
2. How high above the ground does the rock get?
3. What is the velocity of the rock as it passes the top of the cliff on its way to the ground?
4. How long (after being thrown) will it take the rock to reach the ground?
9. A ball is thrown vertically downward from the top of a 220 foot building with an initial velocity of $-22$ feet per second. Find the following:

1. the velocity of the ball after 3 seconds
2. the velocity of the ball after falling 108 feet
10. A four foot tall boy drops a ball from his height above a bridge. The ball hits the water 3 seconds later. How high is the bridge above the water?

11. A ball is thrown vertically upward from a window with an initial velocity of 48 feet per second. If the window is 64 feet above the ground, and assuming an acceleration due to gravity of 32 ft/s$^2$, find the following:

1. the maximum height reached by the ball;
2. the time required for the ball to reach the ground; and
3. the velocity of the ball at the time of impact.
12. A ball is thrown upward from the top of a building with a velocity of 60 ft/sec. Four seconds later, the ball strikes the ground at the base of the building. Find the following:

1. the height of the building;
2. the maximum height reached by the ball; and
3. the velocity of the ball when it strikes the ground.
13. A rock is thrown vertically upward with initial velocity 112 ft/sec from a cliff which is 128 ft high. You may assume the acceleration due to gravity is $-32$ ft/sec$^2$.

1. Find both $v(t)$, the velocity of the rock at time $t$; and $h(t)$, the height of the rock at time $t$.
2. What is the greatest height reached by the rock?
3. With what velocity does the rock hit the ground?
14. A rock is thrown upward from the top of a 40 ft high building. After $3/4$ of a second, the rock reaches its maximum height and then falls to the ground. Find the terminal velocity of the rock.

15. From what height must a ball be dropped in order to strike the ground with a speed of 136 ft/s?

16. A ball rolls down a hill. At time $t$ (in seconds), its velocity is $v(t) = -12t$ (in feet per second). If the initial position of the ball is 96 feet from the bottom of the hill, find the following:

1. $s(t)$, the distance between the ball and the bottom of the hill at time $t$;
2. $a(t)$, the acceleration of the ball at time $t$; and
3. the ball's velocity when it reaches the bottom of the hill.