Question 1

A car moves along a straight road such that its position as a function of time is given by $$x(t) = 4t^2$ + 2t + 1 (in $$meters, with $$t in $$seconds). What is the instantaneous velocity of the car at $$t = 3 s$$?

Accepted Answer

$$v_x = 26 m/s$$

Question 2

Which of the following statements about average velocity and average speed is correct?

Accepted Answer

Average speed is the total distance traveled divided by the total time, while average velocity is the displacement divided by the total time.

Question 3

A runner completes one lap around a 400 m track in 50 s, ending at the starting point. What is the runner's average velocity?

Accepted Answer

$$0 m/s$$

Question 4

A ball is thrown straight up with an initial velocity of $$20 m/s. $$Ignoring air resistance, what is the velocity of the ball when it returns to the thrower's hand?

Accepted Answer

$$-20 m/s$$

Question 5

Which of the following equations is NOT valid for motion with constant acceleration?

Accepted Answer

$$x = x_0$ + v_x t^2$

Question 6

A car accelerates from rest at $$3 m/s$^2$$ along a straight road. How far does it travel in $$5$$ seconds?

Accepted Answer

$$75 m$$

Question 7

A stone is dropped from a cliff and falls freely under gravity. Which of the following statements is true about its motion (neglecting air resistance)?

Accepted Answer

The acceleration is constant and directed downward.

Question 8

On a position-time ($$x$$-$$t) $$graph, what does the slope of the tangent at any point represent?

Accepted Answer

The instantaneous velocity at that point.

Question 9

A car moves with a constant velocity of $$15 m/s $$for $$10 s$$, then accelerates uniformly to $$25 m/s in $$the next $$5 s. $$What is the average acceleration during the acceleration phase?

Accepted Answer

$$1 m/s$^2$$

Question 10

A ball is thrown vertically upward with an initial velocity $$v_0. At $$the highest point of its trajectory, which of the following is true?

Accepted Answer

The velocity is zero and the acceleration is $$-g.$$

Question 11

A cyclist travels $$120 m $$east in $$20 s$$, then $$60 m $$west in $$10 s. $$What is the average velocity for the entire trip?

Accepted Answer

$$2 m/s$\ 	ext{east}$$

Question 12

Which of the following best describes the motion of a freely falling object released from rest (neglecting air resistance)?

Accepted Answer

Its velocity increases linearly with time.

Question 13

A car starts from rest and accelerates uniformly at $$2 m/s$^2$$ for $$8 s. $$What is its final velocity?

Accepted Answer

$$16 m/s$$

Question 14

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$$a_x = \frac{dv_x}{dt}$$

Question 15

A car moves with a velocity given by $$v_x = 10 + 2t (in m/s$$, $$t in s). $$What is the car's acceleration?

Accepted Answer

$$2 m/s$^2$$

Question 16

A ball is dropped from a height of $$45 m. $$How long does it take to reach the ground? (Assume $$g = 9.8 m/s$^2$$ and neglect air resistance.)

Accepted Answer

$$3.03 s$$

Question 17

On a velocity-time ($$v_x$$-$$t) $$graph, what does the area under the curve between two times represent?

Accepted Answer

The displacement during that time interval.

Question 18

A car is moving in the positive $$x-$$direction and slowing down. What are the signs of its velocity and acceleration?

Accepted Answer

Velocity is positive, acceleration is negative.

Question 19

A train starts from rest and accelerates uniformly at $$1 m/s$^2$$ for $$20 s. $$What is the total distance covered by the train in this time?

Accepted Answer

$$400 m$$

Question 20

A ball is thrown downward from a height of $$20 m $$with an initial velocity of $$5 m/s. $$How long does it take to hit the ground? (Take $$g = 9.8 m/s$^2)$$

Accepted Answer

$$1.53 s$$

Motion Along a Straight Line: Kinematics in One Dimension

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