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

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