Q: A car starts from rest at position $$x_0 = 0$ and accelerates at a constant rate a = 2.0$$\ \mathrm{$$m/s^2$$}$$ for t = 5.0$$\ \mathrm{s}$$. Using the equation x$$ = $$x_0$$ + $$v_0 t$$ + \frac{1}{2} a $$t^2$$, what is the car's position after 5 seconds?

$$x = 0 + 0 \times 5 + \frac{1}{2} \times 2.0 \times (5.0)^2$ = 25\ \mathrm{m}$$

Q: A ball is thrown straight up with an initial velocity $$v_0 = 15$$\ \mathrm{m/s}$$. Ignoring air resistance, what is the maximum height reached by the ball? (Use a = -9.8$$\ \mathrm{$$m/s^2$$}$$ and x_0$ = 0)$$

$$x = \frac{v_0$^2}{2|a|} = \frac{(15)^2$}{2 \times 9.8} = 11.5\ \mathrm{m}$$

Q: A stone is dropped from rest from a cliff. How far does it fall in the first 3 seconds? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$x = \frac{1}{2} g t^2$ = \frac{1}{2} \times 9.8 \times 9 = 44.1\ \mathrm{m}$$

Question 1

A car starts from rest at position $$x_0 = 0$ and accelerates at a constant rate a = 2.0$$\ \mathrm{$$m/s^2$$}$$ for t = 5.0$$\ \mathrm{s}$$. Using the equation x$$ = $$x_0$$ + $$v_0 t$$ + \frac{1}{2} a $$t^2$$, what is the car's position after 5 seconds?

Accepted Answer

$$x = 0 + 0 	imes 5 + \frac{1}{2} 	imes 2.0 	imes (5.0)^2$ = 25\ \mathrm{m}$$

Question 2

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total path length traveled, while displacement is the straight-line change in position.

Question 3

A runner moves $$30\ \mathrm{m}$$ east, then $$40\ \mathrm{m}$$ west. What is the runner's displacement?

Accepted Answer

$$10\ \mathrm{m}$$ west

Question 4

If an object moves with constant acceleration, which equation correctly relates its position $$x to $$time $$t$$?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 5

A ball is thrown straight up with an initial velocity $$v_0 = 15$$\ \mathrm{m/s}$$. Ignoring air resistance, what is the maximum height reached by the ball? (Use a = -9.8$$\ \mathrm{$$m/s^2$$}$$ and x_0$ = 0)$$

Accepted Answer

$$x = \frac{v_0$^2}{2|a|} = \frac{(15)^2$}{2 	imes 9.8} = 11.5\ \mathrm{m}$$

Question 6

Which of the following statements about acceleration is correct?

Accepted Answer

Acceleration is the rate of change of velocity.

Question 7

A train moves with a constant velocity of $$20\ \mathrm{m/s}$$ for $$120\ \mathrm{s}. $$What is the displacement of the train?

Accepted Answer

$$2400\ \mathrm{m}$$

Question 8

A car traveling at $$30\ \mathrm{m/s}$$ comes to a stop in $$10\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{v - v_0$}{t} = \frac{0 - 30}{10} = -3\ \mathrm{m/s^2$}$$

Question 9

Which of the following is true about freely falling objects near Earth's surface (ignoring air resistance)?

Accepted Answer

All objects fall with the same acceleration.

Question 10

A stone is dropped from rest from a cliff. How far does it fall in the first 3 seconds? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$x = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 9.8 	imes 9 = 44.1\ \mathrm{m}$$

Question 11

Which of the following best describes instantaneous velocity?

Accepted Answer

It is the velocity at a specific instant, as the time interval approaches zero.

Question 12

A cyclist accelerates from $$5\ \mathrm{m/s} to$$ $$15\ \mathrm{m/s} in$$ $$4\ \mathrm{s}. $$What is the average acceleration?

Accepted Answer

$$a = \frac{15 - 5}{4} = 2.5\ \mathrm{m/s^2$}$$

Question 13

A car moves with an initial velocity $$v_0 = 10$$\ \mathrm{m/s}$$ and accelerates at a = 2$$\ \mathrm{$$m/s^2$$}$$ for t = 6$$\ \mathrm{s}$$. What is its final velocity?

Accepted Answer

$$v = v_0$ + a t = 10 + 2 	imes 6 = 22\ \mathrm{m/s}$$

Question 14

Which of the following is a correct step in solving a kinematics problem?

Accepted Answer

Write down the known and unknown quantities.

Question 15

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

Accepted Answer

Solve $$0 = 20 + 5t - 4.9t^2$; t$$ \approx 1.5\ \mathrm{s}$$

Kinematics in One Dimension: Structured Study Notes

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