Question 1

An object moves along the s-axis with its position given by $$s(t) = 5t^2$ + 3t + 2$$, where $$s is in $$meters and $$t is in $$seconds. What is the object's instantaneous velocity at $$t = 4 s$$?

Accepted Answer

$$v(4) = 43 m/s$$

Question 2

A car starts from rest and accelerates uniformly along a straight road. If its acceleration is $$a = 2 m/s$^2$$, how far does it travel in 5 seconds?

Accepted Answer

$$s = 50 m$$

Question 3

Which of the following best describes the average velocity of an object moving along the s-axis from $$s_1 = 10$ m at t_1$ = 2 s to$$ $$s_2 = 34$ m at t_2$ = 6 s$$?

Accepted Answer

$$v_{avg} = 6 m/s$$

Question 4

Given a velocity-time graph that is a straight line with a positive slope, what can you conclude about the object's motion?

Accepted Answer

The object is accelerating at a constant rate.

Question 5

If the position of an object is given by $$x(t) = 4t^3$ - 2t^2$ + t$$, what is the acceleration at $$t = 2 s$$?

Accepted Answer

$$a(2) = 40 m/s$^2$$

Question 6

A runner's velocity as a function of time is given by $$v(t) = 6 - 2t (in m/s). At $$what time does the runner come to rest?

Accepted Answer

$$t = 3 s$$

Question 7

Which of the following statements about the area under a velocity-time graph is correct?

Accepted Answer

It represents the displacement of the object.

Question 8

A ball is thrown straight up with an initial velocity of $$v_0 = 20$ m/s. Neglecting air resistance, what is the maximum height reached by the ball? (Use g = 10$ m/s^2$.)

Accepted Answer

$$h_{max} = 20 m$$

Question 9

If an object moves according to the power law function $$x(t) = c t^n$$, which of the following expressions gives the instantaneous velocity?

Accepted Answer

$$v(t) = n c t$$^{n-1}$$

Question 10

A cyclist travels 10 km east in 0.5 hours, then 5 km west in 0.25 hours. What is the cyclist's average velocity for the entire trip?

Accepted Answer

$$v_{avg} = 6 km/h $$east

Question 11

Which of the following is true for an object moving with constant acceleration along a straight line?

Accepted Answer

The velocity-time graph is a straight line.

Question 12

A car moves with a velocity given by $$v(t) = 3t^2$ m/s. What is the displacement of the car between t = 0$ s and t = 2$ s?

Accepted Answer

$$x = 16 m$$

Question 13

If the acceleration of an object is zero, which of the following must be true?

Accepted Answer

The velocity is constant.

Question 14

A position-time graph of an object is a straight line with a negative slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving in the negative direction at constant velocity.

Question 15

A train starts from rest and accelerates uniformly at $$a = 1 m/s$^2$$ for 10 seconds. What is its final velocity?

Accepted Answer

$$v = 10 m/s$$

Question 16

Which of the following best describes the relationship between position, velocity, and acceleration for motion along a straight line?

Accepted Answer

Velocity is the derivative of position with respect to time, and acceleration is the derivative of velocity with respect to time.

Question 17

A car moves along a straight road such that its velocity is given by $$v(t) = 10 - t m/s. At $$what time does the car come to a stop?

Accepted Answer

$$t = 10 s$$

Question 18

If the acceleration of an object is given by $$a(t) = 6t$$, and its initial velocity is $$v_0 = 2$ m/s at t = 0$, what is the velocity at t = 3$ s?

Accepted Answer

$$v = 29 m/s$$

Question 19

A position-time graph shows a curve that gets steeper as time increases. What does this indicate about the object's motion?

Accepted Answer

The object is speeding up.

Question 20

A car travels at 20 m/s for 3 seconds, then at 10 m/s for 2 seconds. What is the car's average velocity over the 5 seconds?

Accepted Answer

$$v_{avg} = 16 m/s$$

Kinematics: Motion Along a Straight Line

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