Q: A car travels 100 km east in 2 hours, then 60 km west in 1 hour. What is the car's average velocity over the entire trip?

$$v_{av} = \frac{100\,\text{km} - 60\,\text{km}}{3\,\text{h}} = 13.3\,\text{km/h}$$ east

Q: A ball is thrown straight up with an initial velocity of $$15\,\text{m/s}. $$What is its velocity after $$1\,\text{s}$$? (Take $$g = 9.8\,\text{m/s}^2$$ downward.)

$$v = 15\,\text{m/s} - (9.8\,\text{m/s}^2)(1\,\text{s}) = 5.2\,\text{m/s}$$ upward

Q: A police officer starts from rest and accelerates at $$3.0\,\text{m/s}^2 to $$catch a car moving at $$15\,\text{m/s}$$ with a $$0$$ head start. How long does it take the officer to catch the car?

$$t = \frac{2 v_{M0}}{a_P} = \frac{2 \times 15}{3} = 10\,\text{s}$$

Q: A train moves with constant acceleration. Its initial velocity is $$10\,\text{m/s}$$, and after $$5\,\text{s} it $$reaches $$30\,\text{m/s}. $$What is the acceleration?

$$a = \frac{v - v_0$}{t} = \frac{30 - 10}{5} = 4\,\text{m/s}^2$$

Question 1

A car travels 100 km east in 2 hours, then 60 km west in 1 hour. What is the car's average velocity over the entire trip?

Accepted Answer

$$v_{av} = \frac{100\,	ext{km} - 60\,	ext{km}}{3\,	ext{h}} = 13.3\,	ext{km/h}$$ east

Question 2

Which of the following statements about average speed and average velocity is correct for a round-trip journey?

Accepted Answer

Average speed is positive, but average velocity is zero.

Question 3

A position vs. time graph for an object moving along a straight line 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 with constant velocity.

Question 4

Given the velocity-time graph below, what does the area under the curve between $$t_1$$ and $$t_2$$ represent?

Accepted Answer

The displacement $$\Delta x$$ between $$t_1$$ and $$t_2$$

Question 5

A ball is thrown straight up with an initial velocity of $$15\,	ext{m/s}. $$What is its velocity after $$1\,	ext{s}$$? (Take $$g = 9.8\,	ext{m/s}^2$$ downward.)

Accepted Answer

$$v = 15\,	ext{m/s} - (9.8\,	ext{m/s}^2)(1\,	ext{s}) = 5.2\,	ext{m/s}$$ upward

Question 6

Which kinematic equation would you use to find the final velocity of an object given its initial velocity, constant acceleration, and displacement, but not time?

Accepted Answer

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

Question 7

A police officer starts from rest and accelerates at $$3.0\,	ext{m/s}^2 to $$catch a car moving at $$15\,	ext{m/s}$$ with a $$0$$ head start. How long does it take the officer to catch the car?

Accepted Answer

$$t = \frac{2 v_{M0}}{a_P} = \frac{2 	imes 15}{3} = 10\,	ext{s}$$

Question 8

At the highest point in its trajectory, a ball thrown straight up has:

Accepted Answer

Zero velocity and acceleration $$a = -g$$

Question 9

A train moves with constant acceleration. Its initial velocity is $$10\,	ext{m/s}$$, and after $$5\,	ext{s} it $$reaches $$30\,	ext{m/s}. $$What is the acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{30 - 10}{5} = 4\,	ext{m/s}^2$$

Question 10

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

Accepted Answer

The slope of the tangent to the $$x vs$$. $$t$$ curve at time $$t$$

Question 11

A runner moves along a straight track. Her position as a function of time is $$x(t) = 2t^2$ + 3t. $$What is her instantaneous velocity at $$t = 4\,	ext{s}$$?

Accepted Answer

$$v = \frac{dx}{dt} = 4t + 3 = 4 	imes 4 + 3 = 19\,	ext{m/s}$$

Question 12

A car accelerates from rest at $$2\,	ext{m/s}^2$$ for $$8\,	ext{s}. $$What is its displacement during this time?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$ = 0 + \frac{1}{2} 	imes 2 	imes 8^2$ = 64\,	ext{m}$$

Question 13

Which of the following is true about the acceleration of an object in free fall near Earth's surface (neglecting air resistance)?

Accepted Answer

It is constant and has magnitude $$g = 9.8\,	ext{m/s}^2$$ downward.

Question 14

A velocity vs. time graph for an object is a horizontal line above the time axis. What does this indicate?

Accepted Answer

The object moves with constant positive velocity.

Question 15

A cyclist travels 40 km north in 2 hours, then 30 km south in 1 hour. What is the average speed for the entire trip?

Accepted Answer

$$s_{av} = \frac{40 + 30}{3} = 23.3\,	ext{km/h}$$

Question 16

If the velocity of an object is zero at some instant, which of the following must also be true at that instant?

Accepted Answer

None of the above; acceleration can be zero, positive, or negative.

Question 17

A ball is dropped from rest from a height of $$20\,	ext{m}. $$How long does it take to reach the ground? (Use $$g = 9.8\,	ext{m/s}^2.)$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} \approx 2.02\,	ext{s}$$

Question 18

Which of the following best describes the relationship between the sign of velocity and the direction of motion in 1D kinematics?

Accepted Answer

A positive velocity means motion in the positive direction; a negative velocity means motion in the negative direction.

Motion Along a Straight Line: Kinematics in One Dimension

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