Q: The instantaneous velocity $$v of an $$object at time $$t is $$defined mathematically as:

$$v = \lim_{\Delta t \to 0} \frac{\Delta s}{\Delta t}$$

Question 1

An object moves with uniform motion along a straight line. If its initial position is $$s_i at $$time $$t_i$$ and its velocity is $$v_s$$, what is its final position $$s_f$$ after a time interval $$\Delta t$$?

Accepted Answer

$$s_f = s_i + v_s \Delta t$$

Question 2

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

Accepted Answer

The object is moving with constant positive velocity.

Question 3

A bug zig-zags back and forth on a picnic table from $$x=0 cm to$$ $$x=50 cm as $$shown. What are the bug's distance traveled and displacement?

Accepted Answer

50 cm and -30 cm.

Question 4

The slope at a point on a position-versus-time graph of an object represents:

Accepted Answer

The object's velocity at that point.

Question 5

Given the position function $$s(t) = 2t^2$ m, where t$ is in seconds, what is the particle's velocity at t = 3$ s?

Accepted Answer

$$v = 12 m/s$$

Question 6

Which of the following best describes the area under a velocity-versus-time graph between $$t_i$$ and $$t_f$$?

Accepted Answer

It represents the object's displacement $$\Delta s.$$

Question 7

A car starts at $$x=0 m at$$ $$t=0 s $$and moves with a velocity described by the graph: $$v_x = 4 m/s $$for $$0 \u003c t \u003c 2 s. $$What is the car's position at $$t = 2 s$$?

Accepted Answer

$$x = 8 m$$

Question 8

An object moves with constant acceleration $$a_x. $$Which equation gives its velocity at a later time $$t_f if $$its initial velocity is $$v_{xi}$$?

Accepted Answer

$$v_{xf} = v_{xi} + a_x \Delta t$$

Question 9

A ball is tossed straight up in the air. At its very highest point, the ball's instantaneous acceleration $$a_x is$$:

Accepted Answer

Negative.

Question 10

A ball rolls up a ramp and then rolls down. Which acceleration graph correctly represents its motion?

Accepted Answer

A constant negative acceleration throughout.

Question 11

If the velocity of an object is given by $$v_x = 5 m/s $$for $$t \u003e 0$$, what is the corresponding position-versus-time graph?

Accepted Answer

A straight line with slope $$5.$$

Question 12

A basketball player runs with a velocity that increases linearly from $$0 to$$ $$6 m/s $$over $$3$$ seconds. What is the player's acceleration during this interval?

Accepted Answer

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

Question 13

An object slows down while moving away from the origin. What is the sign of its velocity and acceleration?

Accepted Answer

Velocity is positive, acceleration is negative.

Question 14

A car moves along a straight road and speeds up. What is the sign of its acceleration if its velocity is positive?

Accepted Answer

Positive.

Question 15

The instantaneous velocity $$v of an $$object at time $$t is $$defined mathematically as:

Accepted Answer

$$v = \lim_{\Delta t 	o 0} \frac{\Delta s}{\Delta t}$$

Question 16

If the acceleration of a particle is given by $$a_x = 2 m/s$^2$$ and its initial velocity is $$10 m/s$$, what is its velocity after $$8$$ seconds?

Accepted Answer

$$v = 26 m/s$$

Question 17

Which of the following statements about free fall is correct?

Accepted Answer

In a vacuum, all objects fall at the same rate regardless of mass.

Question 18

A position graph shows a curve with increasing slope. What does this indicate about the object's motion?

Accepted Answer

The object is accelerating.

Question 19

The area under an acceleration-versus-time graph between $$t_i$$ and $$t_f$$ gives:

Accepted Answer

The change in velocity $$\Delta v$$

Question 20

A runner accelerates from rest at $$a = 3 m/s$^2$$ for $$4$$ seconds. What is the runner's final velocity?

Accepted Answer

$$v = 12 m/s$$

Kinematics: Motion in One Dimension – Study Notes

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