Q: A dragster moves from $$x_1 = 19$$\ \text{m}$$ at t_1$ = 1.0\ \text{s} to$$ $$x_2 = 277$$\ \text{m}$$ at t_2$ = 4.0\ \text{s}. $$What is the average x-velocity of the dragster during this interval?

$$v_{\text{av}-x} = \frac{277\ \text{m} - 19\ \text{m}}{4.0\ \text{s} - 1.0\ \text{s}} = 86\ \text{m/s}$$

Q: A truck moves from $$x_1 = 277$$\ \text{m}$$ at t_1$ = 16.0\ \text{s} to$$ $$x_2 = 19$$\ \text{m}$$ at t_2$ = 25.0\ \text{s}. $$What is the average x-velocity of the truck?

$$v_{\text{av}-x} = \frac{19\ \text{m} - 277\ \text{m}}{9.0\ \text{s}} = -28.7\ \text{m/s}$$

Q: Which equation gives the average x-velocity of a particle in straight-line motion during a time interval from $$t_1 to$$ $$t_2$$?

$$v_{\text{av}-x} = \frac{x_2$ - x_1$}{t_2$ - t_1$}$$

Q: A car is initially traveling at $$v_{0x} = 15\ \text{m/s}$$ and begins to accelerate at $$a_x = 2.0\ \text{m/s}^2. $$What is its velocity after $$5.0\ \text{s}$$?

$$v_x = 15\ \text{m/s} + (2.0\ \text{m/s}^2)(5.0\ \text{s}) = 25\ \text{m/s}$$

Q: A motorcyclist starts at $$x_0 = 5.0$$\ \text{m}$$, v$$_{0x} = 15\ \text{m/s}$$, and accelerates at a_x = 4.0$$\ \text{m/s}^2$$. What is his position at t = 2.0$$\ \text{s}$$?

$$x = 5.0\ \text{m} + (15\ \text{m/s})(2.0\ \text{s}) + \frac{1}{2}(4.0\ \text{m/s}^2)(2.0\ \text{s})^2$ = 43\ \text{m}$$

Question 1

A dragster moves from $$x_1 = 19$$\ 	ext{m}$$ at t_1$ = 1.0\ 	ext{s} to$$ $$x_2 = 277$$\ 	ext{m}$$ at t_2$ = 4.0\ 	ext{s}. $$What is the average x-velocity of the dragster during this interval?

Accepted Answer

$$v_{	ext{av}-x} = \frac{277\ 	ext{m} - 19\ 	ext{m}}{4.0\ 	ext{s} - 1.0\ 	ext{s}} = 86\ 	ext{m/s}$$

Question 2

A truck moves from $$x_1 = 277$$\ 	ext{m}$$ at t_1$ = 16.0\ 	ext{s} to$$ $$x_2 = 19$$\ 	ext{m}$$ at t_2$ = 25.0\ 	ext{s}. $$What is the average x-velocity of the truck?

Accepted Answer

$$v_{	ext{av}-x} = \frac{19\ 	ext{m} - 277\ 	ext{m}}{9.0\ 	ext{s}} = -28.7\ 	ext{m/s}$$

Question 3

Which of the following best describes the instantaneous x-velocity at a given point on a position-time graph?

Accepted Answer

It is the slope of the tangent to the $$x$$-$$t$$ curve at that point.

Question 4

A particle has a positive and increasing x-coordinate. According to the rules, what is the sign of its x-velocity?

Accepted Answer

Positive

Question 5

A bicyclist is moving to the left. If the positive x-direction is chosen to the right, what is the sign of the bicyclist's x-velocity?

Accepted Answer

Negative

Question 6

Which equation gives the average x-velocity of a particle in straight-line motion during a time interval from $$t_1 to$$ $$t_2$$?

Accepted Answer

$$v_{	ext{av}-x} = \frac{x_2$ - x_1$}{t_2$ - t_1$}$$

Question 7

A car is initially traveling at $$v_{0x} = 15\ 	ext{m/s}$$ and begins to accelerate at $$a_x = 2.0\ 	ext{m/s}^2. $$What is its velocity after $$5.0\ 	ext{s}$$?

Accepted Answer

$$v_x = 15\ 	ext{m/s} + (2.0\ 	ext{m/s}^2)(5.0\ 	ext{s}) = 25\ 	ext{m/s}$$

Question 8

Which of the following is a typical velocity magnitude for freeway speeds?

Accepted Answer

$$30\ 	ext{m/s}$$

Question 9

If a particle's x-velocity is positive and increasing, what can be said about its x-acceleration?

Accepted Answer

The x-acceleration is positive and the particle is speeding up in the +x-direction.

Question 10

A motorcyclist starts at $$x_0 = 5.0$$\ 	ext{m}$$, v$$_{0x} = 15\ 	ext{m/s}$$, and accelerates at a_x = 4.0$$\ 	ext{m/s}^2$$. What is his position at t = 2.0$$\ 	ext{s}$$?

Accepted Answer

$$x = 5.0\ 	ext{m} + (15\ 	ext{m/s})(2.0\ 	ext{s}) + \frac{1}{2}(4.0\ 	ext{m/s}^2)(2.0\ 	ext{s})^2$ = 43\ 	ext{m}$$

Question 11

On a velocity-time graph, what does the area under the curve represent?

Accepted Answer

The displacement of the particle during the time interval.

Question 12

A particle moves in the -x direction and its x-velocity is negative and decreasing. What is the sign of its x-acceleration?

Accepted Answer

Negative, and the particle is speeding up in the -x direction.

Question 13

If the slope of a position-time graph is zero at a certain point, what does this indicate about the velocity?

Accepted Answer

The velocity is zero at that point.

Question 14

A cheetah's coordinate varies with time according to $$x = 20\ 	ext{m} + (5.0\ 	ext{m/s})t. $$What is its instantaneous velocity?

Accepted Answer

$$v_x = 5.0\ 	ext{m/s}$$

Question 15

Which equation is used to find the position of a particle moving with constant acceleration?

Accepted Answer

$$x = x_0$ + v$$_{0x}$$t + \frac{1}{2}a_xt^2$

Question 16

A particle's x-velocity is positive and decreasing. What is the sign of its x-acceleration?

Accepted Answer

Negative, and the particle is slowing down in the +x direction.

Question 17

A motorcyclist accelerates at $$4.0\ 	ext{m/s}^2$$ and reaches a velocity of $$25\ 	ext{m/s}$$, starting from $$v_{0x} = 15\ 	ext{m/s}. $$How far has he traveled?

Accepted Answer

$$x - x_0$ = \frac{(25\ 	ext{m/s})^2$ - (15\ 	ext{m/s})^2$}{2 	imes 4.0\ 	ext{m/s}^2} = 50\ 	ext{m}$$

Motion Along a Straight Line: Displacement, Velocity, and Acceleration

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드