Q: A train moving at $$75.0\ \mathrm{km/h}$$ applies an emergency brake and comes to rest in $$7.20\ \mathrm{s}. $$How far does the train travel before stopping?

$$d = 75.0\ \mathrm{m/s} \times 7.20\ \mathrm{s} \div 3.6 = 150.0\ \mathrm{m}$$

Q: For a projectile launched at an angle $$\theta$$ with initial velocity $$v_i$$, which equation gives the angle $$\theta in $$terms of $$v_{ix}$$ and $$v_{iy}$$?

$$\theta = \arctan\left(\frac{v_{iy}}{v_{ix}}\right)$$

Question 1

When adding the numbers 12.345 and 6.7, to how many decimal places should the answer be rounded?

Accepted Answer

To the least number of decimal places

Question 2

Which of the following statements about the number 120.0 is correct?

Accepted Answer

All digits are significant

Question 3

Which of the following is true about the speed of an object?

Accepted Answer

Speed is always a scalar quantity

Question 4

An object moving in the negative direction along the x-axis has a velocity of -5 m/s. What does the negative sign indicate?

Accepted Answer

The object is moving in the opposite direction to the positive axis

Question 5

A car is moving in the positive x-direction and has a positive acceleration. Which of the following is always true?

Accepted Answer

The car's velocity is increasing in the positive direction

Question 6

An object thrown upward experiences which type of acceleration until it reaches its peak height?

Accepted Answer

Negative acceleration (downward)

Question 7

Which statement about the magnitude of a vector is correct?

Accepted Answer

The magnitude of a vector is always positive or zero

Question 8

The acceleration of a freely falling object near Earth's surface is:

Accepted Answer

Constant and directed downward

Question 9

Which component(s) of a projectile's motion are affected by gravity?

Accepted Answer

Only the vertical component

Question 10

At the maximum height of a projectile, which of the following is true about its vertical velocity?

Accepted Answer

It is zero

Question 11

Given vectors $$\vec{a}$$ and $$\vec{b}$$ with magnitudes $$a = 3.00\ \mathrm{m}$$ and $$b = 4.00\ \mathrm{m}$$, and $$\vec{c} = p\vec{a} + q\vec{b}$$, if $$\vec{c}$$ has a magnitude of $$10.0\ \mathrm{m}$$ and is at an angle $$30.0^\circ$$ from $$\vec{a}$$, what is the value of $$p if$$ $$q = 2$$?

Accepted Answer

$$p = 2.0$$

Question 12

A commuter train accelerates at $$1.45\ \mathrm{m/s^2$}$$ from rest to a top speed of $$75.0\ \mathrm{km/h}. $$How long does it take to reach top speed?

Accepted Answer

$$t = 25.8\ \mathrm{s}$$

Question 13

A train moving at $$75.0\ \mathrm{km/h}$$ applies an emergency brake and comes to rest in $$7.20\ \mathrm{s}. $$What is the magnitude of the emergency acceleration?

Accepted Answer

$$a = 2.89\ \mathrm{m/s^2$}$$

Question 14

A train moving at $$75.0\ \mathrm{km/h}$$ applies an emergency brake and comes to rest in $$7.20\ \mathrm{s}. $$How far does the train travel before stopping?

Accepted Answer

$$d = 75.0\ \mathrm{m/s} 	imes 7.20\ \mathrm{s} \div 3.6 = 150.0\ \mathrm{m}$$

Question 15

A runner starts at $$x_i = 0\ \mathrm{m} at$$ $$t_i = 0\ \mathrm{s}$$ and follows a velocity vs. time graph. If the velocity is constant at $$2\ \mathrm{m/s}$$ for $$12\ \mathrm{s}$$, what is the runner's position at $$t = 12\ \mathrm{s}$$?

Accepted Answer

$$x = 12\ \mathrm{m}$$

Question 16

A golf ball is struck with an initial velocity $$\vec{v}_i at an $$angle $$	heta$$ above the ground. If the ball reaches a maximum height $$y_{max} = 18.0\ \mathrm{m}$$, what is the vertical component of the initial velocity $$v_{iy}$$?

Accepted Answer

$$v_{iy} = \sqrt{2gy_{max}}$$

Question 17

A golf ball is hit and lands $$x_{max} = 113.0\ \mathrm{m}$$ away. If the time of flight is $$t$$, what is the horizontal component of the initial velocity $$v_{ix}$$?

Accepted Answer

$$v_{ix} = \frac{x_{max}}{t}$$

Question 18

For a projectile launched at an angle $$	heta$$ with initial velocity $$v_i$$, which equation gives the angle $$	heta in $$terms of $$v_{ix}$$ and $$v_{iy}$$?

Accepted Answer

$$	heta = \arctan\left(\frac{v_{iy}}{v_{ix}}ight)$$

Physics Study Guide: Vectors, Kinematics, and Projectile Motion

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