Question 1

A ball is thrown vertically upward from the ground with an initial velocity of $$32 ft/s. $$The height of the ball after $$t$$ seconds is given by $$h(t) = 32t - 16t^2$. What is the maximum height reached by the ball?

Accepted Answer

$$16 ft$$

Question 2

Given the position function $$s(t) = -16t^2$ + 32t$$, what is the velocity of the ball at $$t = 1$$ second?

Accepted Answer

$$0 ft/s$$

Question 3

Suppose the height of a ball is modeled by $$h(t) = -10t^2$ + 50t + 5. $$What is the initial height of the ball?

Accepted Answer

$$5 ft$$

Question 4

A car's position is given by $$s(t) = 5t^2$ - 20t + 10. $$What is the car's velocity at $$t = 3$$ seconds?

Accepted Answer

$$-10 ft/s$$

Question 5

If $$s(t) = 8t^2$ - 2t + 4$$ represents the position of an object, what is the acceleration of the object?

Accepted Answer

$$16$$ $$ft/s^2$$

Question 6

A ball is dropped from a height of $$27 ft. $$Its height after $$t$$ seconds is $$h(t) = 27 - 16t^2$. How long does it take for the ball to hit the ground?

Accepted Answer

$$1.5 s$$

Question 7

Given $$s(t) = -10t^2$ + 50t$$, what is the average velocity of the object from $$t = 0 to$$ $$t = 5$$ seconds?

Accepted Answer

$$0 ft/s$$

Question 8

A ball is thrown upward and its height is given by $$h(t) = -16t^2$ + 64t + 80. $$What is the velocity of the ball when it reaches its maximum height?

Accepted Answer

$$0 ft/s$$

Question 9

If the position of a car is $$s(t) = 2t^2$ + 3t$$, what is the instantaneous velocity at $$t = 4$$ seconds?

Accepted Answer

$$19 ft/s$$

Question 10

A ball is thrown from a building and its height is $$h(t) = -16t^2$ + 32t + 48. $$How long does it take to reach the ground?

Accepted Answer

$$3 s$$

Question 11

Given $$s(t) = -25t^2$ + 50t$$, what is the velocity at $$t = 2$$ seconds?

Accepted Answer

$$-50 ft/s$$

Question 12

A ball is thrown upward with initial velocity $$v_0$$ from a height $$h_0. $$Its height is $$h(t) = -16t^2$ + v_0$ t + h_0$. If v_0$ = 40 ft/s $$and $$h_0 = 10$ ft, what is the maximum height?

Accepted Answer

$$35 ft$$

Question 13

If $$s(t) = 4t^2$ - 8t + 2$$, what is the acceleration of the object?

Accepted Answer

$$8$$ $$ft/s^2$$

Question 14

A ball is dropped from a height of $$80 ft. $$Its height after $$t$$ seconds is $$h(t) = 80 - 16t^2$. How long does it take to hit the ground?

Accepted Answer

$$2.236 s$$

Question 15

Given $$s(t) = -16t^2$ + 64t + 80$$, what is the time when the ball reaches its maximum height?

Accepted Answer

$$2 s$$

Question 16

If the velocity of a ball is $$v(t) = -32t + 32$$, at what time does the ball reach its maximum height?

Accepted Answer

$$1 s$$

Question 17

A ball is thrown upward and its height is $$h(t) = -16t^2$ + 48t + 64. $$What is the initial velocity?

Accepted Answer

$$48 ft/s$$

Question 18

Given $$s(t) = -10t^2$ + 50t + 5$$, what is the velocity at $$t = 0$$?

Accepted Answer

$$50 ft/s$$

Question 19

If $$s(t) = -16t^2$ + 32t$$, what is the acceleration of the ball?

Accepted Answer

$$-16$$ $$ft/s^2$$

Business Calculus: Applications of Derivatives to Motion and Rates of Change

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