Q: A dart is thrown with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following expressions gives the maximum height reached by the dart?

$$h_{max} = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A car rounds a flat curve of radius $$50\ \mathrm{m} at$$ $$20\ \mathrm{m/s}. $$What is the required frictional force if the car's mass is $$1000\ \mathrm{kg}$$?

$$F = \dfrac{mv^2$}{r} = \dfrac{1000 \times 20^2$}{50}$$

Q: A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$\theta. $$Which equation gives the time to reach the ground if the cliff height is $$h$$?

$$t = \dfrac{v_0$ \sin \theta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Question 1

A dart is thrown with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following expressions gives the maximum height reached by the dart?

Accepted Answer

$$h_{max} = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 2

A 5 kg box is pulled horizontally with a force of 20 N. What is the acceleration of the box, assuming no friction?

Accepted Answer

$$a = 4\ \mathrm{m/s^2$}$$

Question 3

A plane flies with an airspeed of $$200\ \mathrm{km/h}$$ due north. There is a wind blowing $$50\ \mathrm{km/h} to $$the east. What is the plane's velocity relative to the ground?

Accepted Answer

$$v = \sqrt{200^2$ + 50^2$}\ \mathrm{km/h}$$,\ direction\ =\ \arctan\left(\dfrac{50}{200}\right)$ east of north

Question 4

An object is projected horizontally from a cliff with initial velocity $$v_0. If $$its $$x$$ and $$y$$ velocity components at a certain time are $$v_x$$ and $$v_y$$, which equation correctly relates these components to the initial velocity and time?

Accepted Answer

$$v_x = v_0$,\ v_y = -gt$

Question 5

Given a position vs. time graph for a moving object, how do you determine the average velocity over a time interval $$\Delta t$$?

Accepted Answer

$$v_{avg} = \dfrac{\Delta x}{\Delta t}$$

Question 6

A force vs. acceleration graph is plotted for an object. If the scale for force is missing, but the acceleration scale is known, how can you find the missing force scale?

Accepted Answer

Use $$F = ma$$ and the slope of the graph to determine the force scale

Question 7

A crate is pulled along a horizontal surface with a force $$F at an $$angle $$	heta$$ above the horizontal. What is the horizontal component of the force that causes acceleration?

Accepted Answer

$$F_x = F \cos 	heta$$

Question 8

An object is thrown upward with initial speed $$v_0. $$How long does it take to reach its maximum height?

Accepted Answer

$$t = \dfrac{v_0$}{g}$$

Question 9

A car travels around an unbanked curve of radius $$r at $$speed $$v. $$What is the minimum coefficient of friction $$\mu$$ required to prevent slipping?

Accepted Answer

$$\mu = \dfrac{v^2$}{gr}$$

Question 10

A 2 kg mass is acted on by a constant force of 10 N for 3 seconds. What is the final velocity if it starts from rest?

Accepted Answer

$$v = 15\ \mathrm{m/s}$$

Question 11

A projectile is launched at $$30^\circ$$ above the horizontal with speed $$20\ \mathrm{m/s}. $$What is the horizontal component of its velocity?

Accepted Answer

$$v_x = 20 \cos 30^\circ$$

Question 12

A position-time graph shows a straight line with positive slope. What does this indicate about the object's motion?

Accepted Answer

The object moves with constant positive velocity

Question 13

A 10 kg sled is pulled with a force of 40 N at $$30^\circ$$ above the horizontal. What is the acceleration of the sled, neglecting friction?

Accepted Answer

$$a = \dfrac{40 \cos 30^\circ}{10}$$

Question 14

A ball is dropped from a height $$h. $$How long does it take to reach the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 15

A car rounds a flat curve of radius $$50\ \mathrm{m} at$$ $$20\ \mathrm{m/s}. $$What is the required frictional force if the car's mass is $$1000\ \mathrm{kg}$$?

Accepted Answer

$$F = \dfrac{mv^2$}{r} = \dfrac{1000 	imes 20^2$}{50}$$

Question 16

A graph of acceleration vs. time for a moving object is given. What does the area under the curve represent?

Accepted Answer

The change in velocity $$\Delta v$$

Question 17

A projectile is launched from a cliff with initial velocity $$v_0 at $$angle $$	heta. $$Which equation gives the time to reach the ground if the cliff height is $$h$$?

Accepted Answer

$$t = \dfrac{v_0$ \sin 	heta + \sqrt{(v_0$ \sin \$$theta)^2$$ + 2gh}}{g}$$

Question 18

A car travels at $$30\ \mathrm{m/s}$$ around a curve of radius $$100\ \mathrm{m}. If $$the coefficient of friction is $$0.6$$, will the car skid? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

Yes, because $$\mu \u003c \dfrac{v^2$}{gr}$$

Question 19

A position-time graph for a runner shows a curve that gets steeper with time. What does this indicate?

Accepted Answer

The runner is accelerating

Physics Study Notes: Kinematics, Dynamics, and Motion Analysis

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