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

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

Q: A springbok accelerates upward at $$35\ \mathrm{m/s}^2$$ for $$0.70\ \mathrm{m}$$, then leaves the ground with velocity $$v_1. $$What is $$v_1$$?

$$v_1$$ = \sqrt{2 \times 35 \times 0.70}$$

Question 1

A car moves along a straight road at a constant velocity. Which of the following statements is TRUE about its position-versus-time graph?

Accepted Answer

The graph is a straight line with a slope equal to the car's velocity.

Question 2

An object moves with uniform motion along the x-axis. If its initial position is $$x_0$$ and its velocity is $$v$$, what is its position $$x$$ after a time interval $$\Delta t$$?

Accepted Answer

$$x = x_0$ + v \Delta t$$

Question 3

A runner travels 100 m east, then 40 m west along a straight track. What is the runner's total distance traveled and displacement?

Accepted Answer

Distance: 140 m, Displacement: 60 m east

Question 4

Which of the following best describes the difference between speed and velocity in one-dimensional motion?

Accepted Answer

Speed is always positive and does not include direction; velocity can be positive or negative and includes direction.

Question 5

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

Accepted Answer

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

Question 6

A position-versus-time graph for an elevator shows a section where the slope is zero. What does this indicate about the elevator's motion?

Accepted Answer

The elevator is at rest.

Question 7

A car backs up for 2 s at $$2.0\ \mathrm{m/s}$$, sits at rest for 2 s, then drives forward at $$5.0\ \mathrm{m/s}$$ for 2 s. What is the total displacement after 6 s?

Accepted Answer

$$10.0\ \mathrm{m}$$

Question 8

The area under a velocity-versus-time graph between $$t_1$$ and $$t_2$$ represents:

Accepted Answer

The object's displacement during that interval.

Question 9

A drag racer starts from rest and accelerates uniformly, reaching a velocity of $$12\ \mathrm{m/s}$$ after $$3.0\ \mathrm{s}. $$What is the displacement during this time?

Accepted Answer

$$18\ \mathrm{m}$$

Question 10

A ball is tossed straight up in the air. At its highest point, what is the ball's instantaneous acceleration?

Accepted Answer

$$a = -g$$

Question 11

A car moving at $$20\ \mathrm{m/s}$$ passes a stationary car that immediately begins accelerating at $$5.0\ \mathrm{m/s}^2. $$How far does the stationary car travel before overtaking the moving car?

Accepted Answer

$$160\ \mathrm{m}$$

Question 12

Which kinematic equation is appropriate for finding the final velocity $$v_f of an $$object with constant acceleration $$a$$ after traveling a displacement $$\Delta x$$ from initial velocity $$v_0$$?

Accepted Answer

$$v_f^2$ = v_0$^2 + 2 a \Delta x$$

Question 13

A springbok accelerates upward at $$35\ \mathrm{m/s}^2$$ for $$0.70\ \mathrm{m}$$, then leaves the ground with velocity $$v_1. $$What is $$v_1$$?

Accepted Answer

$$v_1$$ = \sqrt{2 	imes 35 	imes 0.70}$$

Question 14

An object slides down a frictionless inclined plane at angle $$	heta. $$What is the acceleration along the incline?

Accepted Answer

$$a = g \sin 	heta$$

Question 15

A ball rolls up a ramp, stops, and then rolls back down. What is the sign of its acceleration throughout the motion?

Accepted Answer

Acceleration is always negative.

Question 16

Which of the following is TRUE about free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

All objects fall with the same acceleration, regardless of mass.

Question 17

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

Accepted Answer

The object is accelerating.

Question 18

If the velocity-versus-time graph of an object is a straight line with a positive slope, what can you say about the object's acceleration?

Accepted Answer

Acceleration is constant and positive.

Question 19

A cyclist travels at $$5\ \mathrm{m/s}$$ for 10 s, then at $$10\ \mathrm{m/s}$$ for 5 s. What is the average velocity over the entire trip?

Accepted Answer

$$\frac{5 	imes 10 + 10 	imes 5}{15}$$

Kinematics in One Dimension – Study Notes

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