Question 1

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

Accepted Answer

The acceleration is called centripetal and always points toward the center of the circle.

Question 2

A projectile is launched horizontally from a 100 m high cliff with a speed of 40 m/s. How far from the base of the cliff does it land? (Assume $$g = 9.8 \ \mathrm{m/s^2$})$$

Accepted Answer

$$180 \ \mathrm{m}$$

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

A Ferris wheel with a radius of $$10.0 \ \mathrm{m}$$ rotates counterclockwise. At a certain 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 total acceleration of the passenger at this instant?

Accepted Answer

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

Question 5

In projectile motion, which of the following is TRUE about the horizontal and vertical components of motion?

Accepted Answer

The vertical acceleration is constant and equal to $$-g.$$

Question 6

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

Accepted Answer

A vector pointing inward toward the center and ahead of the normal (combining radial and tangential components).

Question 7

Which of the following best describes the tangential component of acceleration in circular motion?

Accepted Answer

It is due to changes in the magnitude (speed) of velocity.

Question 8

A woman walks across a train at $$3 \ \mathrm{mph}$$ while the train moves forward at $$4 \ \mathrm{mph}. $$What is her speed relative to the ground?

Accepted Answer

$$5 \ \mathrm{mph}$$

Question 9

For small angles $$	heta (in $$radians), which of the following approximations is valid?

Accepted Answer

$$\sin 	heta \approx 	heta$$

Question 10

Which of the following is a real-world application of relative velocity?

Accepted Answer

Mid-air refueling of fighter jets.

Question 11

A car is moving clockwise in a flat circular path and is slowing down. Which statement about its acceleration vector is correct?

Accepted Answer

The acceleration vector points behind the normal (opposite to the direction of motion).

Question 12

What is the formula for the arc length $$s$$ subtended by an angle $$\Delta 	heta in a $$circle of radius $$R$$?

Accepted Answer

$$s = R \cdot \Delta 	heta$$

Question 13

At the top of a projectile's trajectory, what is the vertical component of its velocity?

Accepted Answer

$$v_{y} = 0$$

Question 14

Which of the following best describes the direction of the instantaneous acceleration in uniform circular motion?

Accepted Answer

It is always perpendicular to the velocity and points toward the center.

Question 15

A Ferris wheel passenger is gaining speed at a rate of $$0.500 \ \mathrm{m/s^2$} at $$the highest point. What does this value represent?

Accepted Answer

Tangential acceleration

Question 16

If an object moves in a circle of radius $$R at $$constant speed $$v$$, what is the angular velocity $$\omega$$?

Accepted Answer

$$\omega = \frac{v}{R}$$

Question 17

Which of the following is NOT a correct statement about projectile motion?

Accepted Answer

The vertical acceleration is zero.

Question 18

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

Accepted Answer

A vector pointing inward toward the center and behind the normal (combining radial and tangential components).

Question 19

Which of the following is the correct formula for the magnitude of total acceleration $$a$$ for an object in circular motion with both radial ($$a_r) $$and tangential ($$a_t) $$components?

Accepted Answer

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

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

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