Q: A car is traveling at $$17\ \mathrm{m/s}$$ when the driver accelerates at $$5.3\ \mathrm{m/s^2$}$$ for $$25\ \mathrm{m} in $$the same direction. What is the car's speed after traveling the $$25\ \mathrm{m}$$?

$$v_f = \sqrt{17^2$ + 2 \times 5.3 \times 25} = 28.6\ \mathrm{m/s}$$

Q: A car starts from rest and accelerates at $$4\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{s}$$, then continues at constant speed for another $$10\ \mathrm{s}. $$What is the total distance traveled?

$$x = \frac{1}{2} \times 4 \times 10^2$ + (4 \times 10) \times 10 = 200 + 400 = 600\ \mathrm{m}$$

Q: A car traveling at $$25\ \mathrm{m/s}$$ sees a moose and applies the brakes, decelerating at $$8.3\ \mathrm{m/s^2$}. If $$the driver's reaction time is $$0.60\ \mathrm{s}$$, what is the total distance traveled before stopping?

$$d = v_0$ t_{reaction} + \frac{v_0$^2}{2a} = 25 \times 0.6 + \frac{25^2$}{2 \times 8.3} = 15 + 37.65 = 52.65\ \mathrm{m}$$

Q: A ball is thrown directly upwards with an initial velocity of $$30.0\ \mathrm{m/s}. $$What is the maximum height it will reach?

$$h = \frac{v_0$^2}{2g} = \frac{30^2$}{2 \times 9.81} = 45.9\ \mathrm{m}$$

Q: A feather is dropped on the moon from a height of $$1.40\ \mathrm{m}. $$The acceleration due to gravity is $$1.67\ \mathrm{m/s^2$}. $$How long does it take to reach the surface?

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 1.40}{1.67}} = 1.30\ \mathrm{s}$$

Q: A person can jump to a height of $$2.62\ \mathrm{m}. $$What is the takeoff speed?

$$v_0$$ = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 2.62} = 7.17\ \mathrm{m/s}$$

Q: Jill hikes up a hill at $$3.0\ \mathrm{m/s}$$ with a horizontal component of velocity $$2.5\ \mathrm{m/s}. $$What is the angle of the hill?

$$\theta = \cos$$^{-1}$$ \left( \frac{2.5}{3.0} \right) = 33.6^\circ$$

Q: A hiker climbs a $$34^\circ$$ slope at $$0.75\ \mathrm{m/s}$$ for one minute. What vertical distance does he gain?

$$\Delta y = v \sin \theta \times t = 0.75 \times \sin(34^\circ) \times 60 = 25.1\ \mathrm{m}$$

Question 1

A car is traveling at $$17\ \mathrm{m/s}$$ when the driver accelerates at $$5.3\ \mathrm{m/s^2$}$$ for $$25\ \mathrm{m} in $$the same direction. What is the car's speed after traveling the $$25\ \mathrm{m}$$?

Accepted Answer

$$v_f = \sqrt{17^2$ + 2 	imes 5.3 	imes 25} = 28.6\ \mathrm{m/s}$$

Question 2

A car starts from rest and accelerates at $$4\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{s}$$, then continues at constant speed for another $$10\ \mathrm{s}. $$What is the total distance traveled?

Accepted Answer

$$x = \frac{1}{2} 	imes 4 	imes 10^2$ + (4 	imes 10) 	imes 10 = 200 + 400 = 600\ \mathrm{m}$$

Question 3

A car traveling at $$25\ \mathrm{m/s}$$ sees a moose and applies the brakes, decelerating at $$8.3\ \mathrm{m/s^2$}. If $$the driver's reaction time is $$0.60\ \mathrm{s}$$, what is the total distance traveled before stopping?

Accepted Answer

$$d = v_0$ t_{reaction} + \frac{v_0$^2}{2a} = 25 	imes 0.6 + \frac{25^2$}{2 	imes 8.3} = 15 + 37.65 = 52.65\ \mathrm{m}$$

Question 4

A ball is thrown directly upwards with an initial velocity of $$30.0\ \mathrm{m/s}. $$What is the maximum height it will reach?

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{30^2$}{2 	imes 9.81} = 45.9\ \mathrm{m}$$

Question 5

A feather is dropped on the moon from a height of $$1.40\ \mathrm{m}. $$The acceleration due to gravity is $$1.67\ \mathrm{m/s^2$}. $$How long does it take to reach the surface?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 1.40}{1.67}} = 1.30\ \mathrm{s}$$

Question 6

A person can jump to a height of $$2.62\ \mathrm{m}. $$What is the takeoff speed?

Accepted Answer

$$v_0$$ = \sqrt{2gh} = \sqrt{2 	imes 9.81 	imes 2.62} = 7.17\ \mathrm{m/s}$$

Question 7

Which equation correctly relates final velocity, initial velocity, acceleration, and displacement for 1D motion?

Accepted Answer

$$v_f^2$ = v_0$^2 + 2a \Delta x$$

Question 8

An object moves in a straight line with constant acceleration. Which kinematic equation gives its position after time $$t$$?

Accepted Answer

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

Question 9

A vector $$\vec{A}$$ has magnitude $$A$$ and makes an angle $$	heta$$ with the x-axis. What is its x-component?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 10

Jill hikes up a hill at $$3.0\ \mathrm{m/s}$$ with a horizontal component of velocity $$2.5\ \mathrm{m/s}. $$What is the angle of the hill?

Accepted Answer

$$	heta = \cos$$^{-1}$$ \left( \frac{2.5}{3.0} ight) = 33.6^\circ$$

Question 11

A hiker climbs a $$34^\circ$$ slope at $$0.75\ \mathrm{m/s}$$ for one minute. What vertical distance does he gain?

Accepted Answer

$$\Delta y = v \sin 	heta 	imes t = 0.75 	imes \sin(34^\circ) 	imes 60 = 25.1\ \mathrm{m}$$

Question 12

A projectile is launched at $$28\ \mathrm{m/s} at$$ $$40^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{0y} = 28 \sin(40^\circ) = 18.0\ \mathrm{m/s}$$

Question 13

A T-shirt is fired horizontally from a gun at $$28\ \mathrm{m/s}$$ and lands $$60\ \mathrm{m}$$ away. How long does it take to reach the fan?

Accepted Answer

$$t = \frac{60}{28} = 2.14\ \mathrm{s}$$

Question 14

In projectile motion, which statement is true about horizontal acceleration (neglecting air resistance)?

Accepted Answer

Horizontal acceleration is zero.

Question 15

A projectile is launched at $$22.0\ \mathrm{m/s} at$$ $$63^\circ$$ above the horizontal. What is the initial horizontal component of velocity?

Accepted Answer

$$v_{0x} = 22.0 \cos(63^\circ) = 9.98\ \mathrm{m/s}$$

Question 16

Which of the following best describes the path of a projectile launched at an angle (neglecting air resistance)?

Accepted Answer

A parabola

Question 17

Which kinematic equation is most appropriate for finding the time it takes an object to fall a certain vertical distance under constant acceleration?

Accepted Answer

$$y = y_0$ + v_0$ t + \frac{1}{2} a t^2$

Kinematics and Projectile Motion: Study Notes for College Physics

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