Q: A car is cruising at 15 m/s. The driver accelerates at $$2.0\ \mathrm{m/s^2$}$$ for 5.0 s. What distance does the car travel during this period?

$$d = v_0$ t + \frac{1}{2} a t^2$ = 15 \times 5 + 0.5 \times 2.0 \times 25 = 75 + 25 = 100\ \mathrm{m}$$

Q: A cheetah sprints at $$20.0\ \mathrm{m/s}$$ and slows to a stop in $$5.00\ \mathrm{s}. $$What distance does it cover while decelerating?

$$d = \frac{1}{2} (v_0$ + v) t = \frac{1}{2} (20.0 + 0) \times 5.00 = 50.0\ \mathrm{m}$$

Q: A vector has components $$A_x = -8$$ units and $$A_y = 6$$ units. What angle does this vector make with the positive x-axis?

$$\theta = \arctan\left(\frac{A_y}{A_x}\right) = \arctan\left(\frac{6}{-8}\right) \approx -37$$^{\circ}$$ (measured clockwise from x-axis)

Q: A force $$F$$ has a magnitude of $$25.0\ \mathrm{N}$$ and points at an angle of $$30^{\circ}$$ north of east. What is the northward (y) component of this force?

$$F_y = F \sin \theta = 25.0 \sin 30$$^{\circ}$$ = 12.5\ \mathrm{N}$$

Question 1

Which of the following best describes the difference between distance and displacement for a runner who jogs 8 m east and then 3 m west along a straight path?

Accepted Answer

Distance = 11 m, Displacement = 5 m east

Question 2

A car is cruising at 15 m/s. The driver accelerates at $$2.0\ \mathrm{m/s^2$}$$ for 5.0 s. What distance does the car travel during this period?

Accepted Answer

$$d = v_0$ t + \frac{1}{2} a t^2$ = 15 	imes 5 + 0.5 	imes 2.0 	imes 25 = 75 + 25 = 100\ \mathrm{m}$$

Question 3

A cheetah sprints at $$20.0\ \mathrm{m/s}$$ and slows to a stop in $$5.00\ \mathrm{s}. $$What distance does it cover while decelerating?

Accepted Answer

$$d = \frac{1}{2} (v_0$ + v) t = \frac{1}{2} (20.0 + 0) 	imes 5.00 = 50.0\ \mathrm{m}$$

Question 4

Given the equation $$x = vt - 2a/t^2$, where x$ is displacement, v$ is velocity, a$ is acceleration, and t$ is time, is this equation dimensionally correct?

Accepted Answer

No, because $$vt$$ has dimensions of length, but $$2a/t^2$$ has dimensions of $$L/T^2$$ \div $$T^2$$ = $$L/T^4$$, which is not length.

Question 5

A vector has components $$A_x = -8$$ units and $$A_y = 6$$ units. What angle does this vector make with the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{A_y}{A_x}ight) = \arctan\left(\frac{6}{-8}ight) \approx -37$$^{\circ}$$ (measured clockwise from x-axis)

Question 6

If all components of a vector are negative, what can be said about the magnitude of the vector?

Accepted Answer

The magnitude is always positive.

Question 7

A force $$F$$ has a magnitude of $$25.0\ \mathrm{N}$$ and points at an angle of $$30^{\circ}$$ north of east. What is the northward (y) component of this force?

Accepted Answer

$$F_y = F \sin 	heta = 25.0 \sin 30$$^{\circ}$$ = 12.5\ \mathrm{N}$$

Question 8

A car moves along a straight road. Its velocity at $$t = 0 is$$ $$20\ \mathrm{m/s}$$ east. It comes to a stop after $$8\ \mathrm{s}$$, then accelerates in the opposite direction (west) and reaches $$16\ \mathrm{m/s}$$ after another $$4\ \mathrm{s}. $$What is the average acceleration for the entire motion? Take east as positive.

Accepted Answer

$$a_{avg} = \frac{v_f - v_i}{t} = \frac{-16 - 20}{12} = \frac{-36}{12} = -3.0\ \mathrm{m/s^2$}$$

Question 9

Which statement about acceleration is correct?

Accepted Answer

If velocity is negative and acceleration is negative, the object speeds up in the negative direction.

Question 10

A duck starts running from rest and accelerates uniformly along a straight path. It covers $$2.0\ \mathrm{m} in $$the first second. How far will it be after $$5$$ seconds?

Accepted Answer

$$x = \frac{1}{2} a t^2$, \ a = \frac{2.0}{1^2$} \Rightarrow x = 0.5 	imes 2.0 	imes 25 = 25\ \mathrm{m}$

Question 11

Which of the following is true about the average velocity of an object for a round trip between two points?

Accepted Answer

It is always zero.

Question 12

A ball is moving to the left with a velocity of $$-6\ \mathrm{m/s}$$ when it is observed to be gradually coming to rest. What can you conclude about the direction of its acceleration?

Accepted Answer

Acceleration is positive (to the right) until it stops.

Question 13

How many significant figures are in the number 0.040?

Accepted Answer

2

Question 14

Which of the following is the correct result for $$\frac{72.0 - 15.60}{0.982 + 4.3}$$ with the correct number of significant figures?

Accepted Answer

11.6

Question 15

Which velocity-time graph best matches an object that moves rightward, slows to a stop, then moves leftward?

Accepted Answer

A graph that starts positive, decreases to zero, then becomes negative.

Question 16

At the instant an object stops (velocity = 0) after moving rightward and slowing down, which is true?

Accepted Answer

Velocity = 0, Acceleration $$
eq 0$$

PHYS1403: Practice Problems and Concepts in 1D Kinematics and Measurement

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