Q: A dragster moves along a straight track. Its position as a function of time is given by $$x(t) = 100 + 20t + 5t^2$. What is its instantaneous velocity at t = 3$$\ \mathrm{s}$$?

$$v = 20 + 10 \times 3 = 50\ \mathrm{m/s}$$

Q: A car accelerates from rest with a constant acceleration $$a = 2\ \mathrm{m/s^2$}. $$How far does it travel in $$5\ \mathrm{s}$$?

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} \times 2 \times 25 = 25\ \mathrm{m}$$

Q: A ball is dropped from rest from a height of $$45\ \mathrm{m}. $$What is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 45} \approx 29.7\ \mathrm{m/s}$$

Question 1

Which of the following statements correctly distinguishes between distance and displacement?

Accepted Answer

Distance is the total length of travel and always positive, while displacement is the change in position and can be positive, negative, or zero.

Question 2

A car moves from $$x_i = +4\ \mathrm{m} to$$ $$x_f = -1\ \mathrm{m} in$$ $$2\ \mathrm{s}. $$What is the car's average velocity?

Accepted Answer

$$-2.5\ \mathrm{m/s}$$

Question 3

Which equation gives the instantaneous velocity $$v at $$time $$t$$ for motion with constant acceleration $$a$$ and initial velocity $$v_0$$?

Accepted Answer

$$v = v_0$ + a t$$

Question 4

A ball is thrown straight upward from the top of a building with velocity $$v_0. At $$its highest point, which of the following is true?

Accepted Answer

The velocity is zero and the acceleration is negative.

Question 5

Which of the following best describes the graphical meaning of average velocity on a position vs. time plot?

Accepted Answer

The slope of the straight line connecting two points.

Question 6

A dragster moves along a straight track. Its position as a function of time is given by $$x(t) = 100 + 20t + 5t^2$. What is its instantaneous velocity at t = 3$$\ \mathrm{s}$$?

Accepted Answer

$$v = 20 + 10 	imes 3 = 50\ \mathrm{m/s}$$

Question 7

Which of the following is the correct SI unit for acceleration?

Accepted Answer

$$\mathrm{m/s^2$}$$

Question 8

A car accelerates from rest with a constant acceleration $$a = 2\ \mathrm{m/s^2$}. $$How far does it travel in $$5\ \mathrm{s}$$?

Accepted Answer

$$x = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2 	imes 25 = 25\ \mathrm{m}$$

Question 9

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

Accepted Answer

All objects fall with the same constant acceleration $$g$$ regardless of mass.

Question 10

A police car starts from rest and accelerates at $$a_p = 2.0\ \mathrm{m/s^2$}. A $$speeder moves at a constant $$v_s = 30\ \mathrm{m/s}. $$How far does the police car travel before catching up with the speeder?

Accepted Answer

$$x = \frac{v_s^2$}{2 a_p} = \frac{900}{4} = 225\ \mathrm{m}$$

Question 11

Which formula relates velocity, acceleration, and displacement for motion with constant acceleration?

Accepted Answer

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

Question 12

A ball is dropped from rest from a height of $$45\ \mathrm{m}. $$What is its speed just before hitting the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 45} \approx 29.7\ \mathrm{m/s}$$

Question 13

Which statement about deceleration is correct?

Accepted Answer

Deceleration refers to decreasing speed and occurs when velocity and acceleration have opposite signs.

Question 14

On a velocity vs. time graph, what does the slope of the tangent line at a point represent?

Accepted Answer

The instantaneous acceleration at that point.

Question 15

A rocket rises with constant acceleration to a height of $$3.2\ \mathrm{m}$$, reaching a speed of $$26.0\ \mathrm{m/s}. $$What was the rocket's acceleration?

Accepted Answer

$$a = \frac{v^2$}{2x} = \frac{(26.0)^2$}{2 	imes 3.2} \approx 105.6\ \mathrm{m/s^2$}$$

Question 16

Which of the following is NOT a correct step in the problem-solving strategy for kinematics?

Accepted Answer

Ignore units to simplify calculations.

Question 17

If the position of an object is given by $$x(t) = 4t^2$ - 2t + 1$$, what is its instantaneous acceleration?

Accepted Answer

$$a = \frac{d^2$x}{dt^2$} = 8$$

Question 18

A person at the equator travels a distance of $$2\pi R_{Earth} in 24 $$hours due to Earth's rotation. What is their average velocity over this period?

Accepted Answer

$$0\ \mathrm{m/s}$$

Chapter 2: Motion Along a Straight Line – Study Notes

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드