Q: Which of the following is the correct formula for average speed?

$$v_{avg} = \frac{\text{distance traveled}}{\text{time taken}}$$

Question 1

A sprinter's position as a function of time is given by $$x(t) = 6t^2$ - t^3$. What is the instantaneous velocity of the sprinter at t = 2$ s?

Accepted Answer

$$v = 12 m/s$$

Question 2

Which of the following statements best describes the instantaneous velocity at a given time $$t$$?

Accepted Answer

It is the slope of the tangent to the position vs. time graph at time $$t.$$

Question 3

A rocket's velocity as a function of time is shown in a graph. At $$t = 9 s$$, the velocity changes from $$4 m/s to$$ $$0 m/s $$over $$4$$ seconds. What is the instantaneous acceleration at $$t = 9 s$$?

Accepted Answer

$$a = -1 m/s$^2$$

Question 4

A motion diagram of a runner shows equally spaced dots along the path. What does this indicate about the runner's motion?

Accepted Answer

The runner is moving at constant velocity.

Question 5

Given the position function $$x(t) = 6t^2$ - t^3$, what is the acceleration at t = 2$ s?

Accepted Answer

$$a = -6$$ $$m/s^2$

Question 6

A water balloon falls past a 30 cm-high window in $$0.22 s. $$Assuming it was dropped from rest, what is the speed of the balloon as it passes the window?

Accepted Answer

$$v = 1.36 m/s$

Question 7

Which of the following is the correct formula for average speed?

Accepted Answer

$$v_{avg} = \frac{	ext{distance traveled}}{	ext{time taken}}$$

Question 8

If a parachutist falls $$50 m$$, then decelerates at $$20 m/s$^2$$ and reaches the ground with a speed of $$3.0 m/s$$, what kinematic equation would you use to find the time spent decelerating?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 9

The area under a velocity vs. time graph represents which physical quantity?

Accepted Answer

Displacement

Question 10

Which of the following is the correct expression for the definite integral of $$f(x)$$ from $$a to$$ $$b$$?

Accepted Answer

$$\int_a^b f(x) dx = F(b) - F(a)$$

Question 11

A position vs. time graph shows a curve. How do you determine the instantaneous speed at a particular time?

Accepted Answer

Find the slope of the tangent to the curve at that time.

Question 12

A student calculates the average velocity between $$t = 10 s $$and $$t = 17 s as$$ $$0 m/s$$, but the average speed as $$0.57 m/s. $$What does this indicate about the motion?

Accepted Answer

The object returned to its starting position but traveled a distance.

Question 13

Which of the following is NOT a correct use of integration in kinematics?

Accepted Answer

Finding acceleration from position vs. time graph.

Question 14

If $$v(t) = 12 - 6t$$, what is the displacement between $$t = 0$$ and $$t = 2 s$$?

Accepted Answer

$$x = 16 m$$

Question 15

A runner's motion diagram shows increasing spacing between dots. What does this indicate?

Accepted Answer

The runner is accelerating.

Question 16

Which of the following is the correct indefinite integral of $$x^n$$ with respect to $$x$$?

Accepted Answer

$$\int x^n dx = \frac{x$$^{n+1}$$}{n+1} + c$$

Question 17

A position vs. time graph is concave down. What does this indicate about the acceleration?

Accepted Answer

Acceleration is negative.

Question 18

If the velocity of a particle is given by $$v(t) = 12 - 6t$$, what is the position function $$x(t)$$ assuming $$x(0) = 0$$?

Accepted Answer

$$x(t) = 12t - 3t^2$

Question 19

A student integrates $$v(t)$$ from $$t_1 to$$ $$t_2 to $$find displacement. What must they do after finding the antiderivative?

Accepted Answer

Subtract the value at $$t_1$$ from the value at $$t_2.$$

Linear Motion: Position, Velocity, Acceleration, and Integration in Physics

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