Q: In a plane polar coordinate system, a point is specified by which two quantities?

Radial distance $$r$$ and angle $$\theta$$

Question 1

Which of the following equations is dimensionally correct for the distance $$x an $$object travels in time $$t$$, given mass $$m$$ $$[M]$$, speed $$v$$ $$[L/T]$$, and acceleration $$a$$ $$[L/T^2$]$$?

Accepted Answer

$$x = v t + \frac{1}{2} a t^2$

Question 2

A car travels 250 km to a city and returns to its starting point in a total time of 5.00 h. What is the car's average velocity for the entire trip?

Accepted Answer

$$0\ \mathrm{km/h}$$

Question 3

Which of the following best describes the difference between speed and velocity?

Accepted Answer

Speed is a scalar and velocity is a vector.

Question 4

Given a position vs. time graph, what does the slope of the tangent line at a point represent?

Accepted Answer

The instantaneous velocity at that point.

Question 5

A motorcycle starts from rest and accelerates at $$4.20\ \mathrm{m/s^2$}. A $$car passes by at $$15.0\ \mathrm{m/s}$$ and continues at that speed. How long does it take for the motorcycle to catch up to the car?

Accepted Answer

$$7.14\ \mathrm{s}$$

Question 6

Which of the following is the correct equation for displacement $$\Delta x$$ under constant acceleration, given initial velocity $$v_0$$, acceleration $$a$$, and time $$t$$?

Accepted Answer

$$\Delta x = v_0$ t + \frac{1}{2} a t^2$

Question 7

A velocity vs. time graph is a straight line with a nonzero slope. What does this indicate about the motion?

Accepted Answer

The object is moving with constant acceleration.

Question 8

If an object’s velocity and acceleration are in opposite directions, what happens to the object’s speed?

Accepted Answer

The speed decreases.

Question 9

Which of the following statements about displacement is correct?

Accepted Answer

Displacement is a vector quantity.

Question 10

A car moves in a straight line with negative velocity and negative acceleration. Which statement is correct?

Accepted Answer

The car is moving in the negative direction with increasing speed.

Question 11

Which of the following is NOT a requirement for a coordinate system?

Accepted Answer

A specified mass for the origin.

Question 12

In a plane polar coordinate system, a point is specified by which two quantities?

Accepted Answer

Radial distance $$r$$ and angle $$	heta$$

Question 13

Which trigonometric identity correctly relates the sides of a right triangle?

Accepted Answer

$$\sin 	heta = \frac{y}{r}$$

Question 14

A position vs. time graph for an object is a straight line with a positive slope. What does this indicate?

Accepted Answer

The object is moving with constant positive velocity.

Question 15

Which of the following equations gives the instantaneous velocity $$v as a $$function of time $$t$$ for constant acceleration $$a$$ and initial velocity $$v_0$$?

Accepted Answer

$$v = v_0$ + a t$$

Question 16

A runner accelerates from rest at $$2.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What is the runner's final velocity?

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 17

Which of the following statements about dimensional analysis is correct?

Accepted Answer

It can be used to check the consistency of units in equations.

Question 18

If the area under a velocity vs. time graph is calculated, what physical quantity does it represent?

Accepted Answer

Displacement

Question 19

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is its velocity after $$2.0\ \mathrm{s}$$? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$0.4\ \mathrm{m/s}$$\ (upward)

Question 20

Which of the following is a correct statement about average velocity?

Accepted Answer

Average velocity is the total displacement divided by the total time.

Physics with Calculus: Kinematics, Coordinate Systems, and Motion Analysis

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