Question 1

Which of the following statements about uniform circular motion is correct?

Accepted Answer

The acceleration is always directed toward the center and is called centripetal acceleration.

Question 2

A projectile is launched horizontally from a cliff 100 m above the ground with a velocity of 40 m/s. How far from the base of the cliff will it land? Use $$g = 9.8 \mathrm{\ m/s^2$}.$$

Accepted Answer

$$180.0\ \mathrm{m}$$

Question 3

Which equation correctly gives the magnitude of the radial (centripetal) acceleration for an object moving at speed $$v in a $$circle of radius $$r$$?

Accepted Answer

$$a_r = \frac{v^2$}{r}$$

Question 4

In projectile motion, which statement is true about the horizontal and vertical components of motion?

Accepted Answer

The horizontal motion is at constant velocity, while the vertical motion is under constant acceleration.

Question 5

A Ferris wheel with radius $$10.0\ \mathrm{m}$$ rotates counterclockwise. At a given instant, a passenger at the highest point is moving at $$3.00\ \mathrm{m/s}$$ and gaining speed at $$0.500\ \mathrm{m/s^2$}. $$What is the magnitude of the total acceleration?

Accepted Answer

$$1.03\ \mathrm{m/s^2$}$$

Question 6

For small angles $$	heta$$, which approximation is valid for $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta \approx 	heta$$

Question 7

A car travels clockwise in a flat circular path with increasing speed. Which direction best represents the acceleration vector at point P?

Accepted Answer

Direction $$d_2$$

Question 8

Which of the following is an example of non-uniform circular motion?

Accepted Answer

A roller coaster speeding up and slowing down in a vertical loop.

Question 9

What does the value $$0.500\ \mathrm{m/s^2$}$$ represent for a passenger on a Ferris wheel who is gaining speed?

Accepted Answer

Tangential acceleration

Question 10

If an object moves in a circle of radius $$R$$ and subtends an angle $$\Delta 	heta$$, what is the arc length $$s$$?

Accepted Answer

$$s = R \Delta 	heta$$

Question 11

A slow train is traveling at $$4\ \mathrm{mph} in a $$straight line. A woman on the train walks from one side to the other at $$3\ \mathrm{mph}. $$What is her speed and direction relative to an observer at rest, assuming the direction of travel is along $$y$$ and the transverse direction is $$x$$?

Accepted Answer

Speed: $$5\ \mathrm{mph}$$, direction: $$53^\circ$$

Question 12

In circular motion, what is the direction of the instantaneous acceleration vector?

Accepted Answer

Perpendicular to the velocity vector.

Question 13

Which formula gives the magnitude of total acceleration for a particle moving on a curved path with both radial and tangential components?

Accepted Answer

$$a = \sqrt{a_r^2$ + a_t^2$}$$

Question 14

Which of the following is NOT an application of relative velocity?

Accepted Answer

Measuring the mass of an object

Question 15

At the top of a projectile's trajectory, what is true about its velocity and acceleration?

Accepted Answer

Vertical velocity is zero, vertical acceleration is $$-g.$$

Question 16

A car travels clockwise in a flat circular path with decreasing speed. Which arrow best represents the acceleration vector at point P?

Accepted Answer

Direction $$d_3$$

Question 17

As an object moves in a counterclockwise direction along a circular path, its acceleration vector continuously points toward point S. At which point is the object slowing down?

Accepted Answer

All of them

Question 18

What is the tangential acceleration $$a_t$$ for a particle moving on a curved path if its speed changes at a rate $$\frac{dv}{dt}$$?

Accepted Answer

$$a_t = \frac{dv}{dt}$$

Question 19

Which of the following best describes the frame of reference in relative velocity problems?

Accepted Answer

A coordinate system plus a time scale.

Projectile Motion, Circular Motion, and Relative Velocity – Study Notes

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