Question 1

An object moves along a straight line with position function $$s(t) = -4.9t^2$ + 34t + 25$$, where $$s is in $$meters and $$t is in $$seconds. What is the average velocity of the object over the interval $$[0,8]$$?

Accepted Answer

$$-5.2 m/s$$

Question 2

Given the position function $$s(t) = -4.9t^2$ + 34t + 25$$, what is the average velocity of the object over the interval $$[0,6]$$?

Accepted Answer

$$4.6 m/s$$

Question 3

For the position function $$s(t) = -4.9t^2$ + 34t + 25$$, what is the average velocity over the interval $$[0,4]$$?

Accepted Answer

$$14.4 m/s$$

Question 4

The average velocity of an object moving along a line from $$t=a to$$ $$t=b is $$given by which formula?

Accepted Answer

$$\frac{s(b) - s(a)}{b - a}$$

Question 5

If $$s(2) = 150$$ and $$s(5) = 240$$, what is the average velocity of the object over the interval $$[2,5]$$?

Accepted Answer

$$30$$ 	ext{ units/time}

Question 6

The slope of the secant line through the points $$(a, f(a))$$ and $$(b, f(b)) on $$the graph of $$f is $$given by:

Accepted Answer

$$\frac{f(b) - f(a)}{b - a}$$

Question 7

A ball is thrown upward with position $$s(t) = -4.9t^2$ + 34t + 25. $$What is the average velocity between $$t=2$$ and $$t=6$$?

Accepted Answer

$$0.2$$ 	ext{ m/s}

Question 8

Suppose the position of a car is given by $$s(t) = 3t^2$ - 2t + 5. $$What is the average velocity of the car from $$t=1 to$$ $$t=4$$?

Accepted Answer

$$13$$ 	ext{ units/time}

Question 9

A runner's position is given by $$s(t) = 2t^2$ + 3t. $$What is the average velocity between $$t=0$$ and $$t=5$$?

Accepted Answer

$$13$$ 	ext{ units/time}

Question 10

If the average velocity of an object over $$[a,b] is $$negative, what does this indicate about the object's motion?

Accepted Answer

The object is moving in the negative direction on average over $$[a,b]$$

Question 11

Given $$s(t) = -4.9t^2$ + 34t + 25$$, what is the average velocity over the interval $$[2,4]$$?

Accepted Answer

$$24.6$$ 	ext{ m/s}

Question 12

A car travels such that its position at time $$t is$$ $$s(t) = 10t^2$ - 5t + 2. $$What is the average velocity from $$t=0 to$$ $$t=3$$?

Accepted Answer

$$20.5$$ 	ext{ units/time}

Question 13

If $$s(t) is $$the position function of an object, which of the following best describes the meaning of the average velocity over $$[a,b]$$?

Accepted Answer

The change in position divided by the change in time over $$[a,b]$$

Question 14

A cyclist's position is given by $$s(t) = 5t^2$ + 2t. $$What is the average velocity from $$t=1 to$$ $$t=3$$?

Accepted Answer

$$22$$ 	ext{ units/time}

Question 15

If the position of a particle is $$s(t) = t^3$ - 6t^2$ + 9t$$, what is the average velocity from $$t=0 to$$ $$t=3$$?

Accepted Answer

$$0$$ 	ext{ units/time}

Question 16

A rocket's height is given by $$s(t) = 100t - 4.9t^2$. What is the average velocity from t=0$ to t=10$?

Accepted Answer

$$51$$ 	ext{ m/s}

Question 17

If $$s(t) = -4.9t^2$ + 34t + 25$$, what is the average velocity over $$[0,2]$$?

Accepted Answer

$$29.6$$ 	ext{ m/s}

Question 18

A car's position is $$s(t) = 2t^2$ - 4t + 1. $$What is the average velocity from $$t=2 to$$ $$t=5$$?

Accepted Answer

$$6$$ 	ext{ units/time}

Question 19

Which of the following statements is true about the average velocity of an object over an interval $$[a,b]$$?

Accepted Answer

It is equal to the slope of the secant line connecting $$(a, s(a))$$ and $$(b, s(b)) on $$the position-time graph.

Average Velocity and Secant Line Slope in Calculus

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