Q: A car is cruising down a straight road at 15 m/s. To overtake a slower vehicle, the driver steps on the accelerator and achieves a constant acceleration of 2.0 m/s$$^2. $$After 5.0 s, the car reaches 25 m/s. How far does the car travel during this period of acceleration?

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

Q: If the components of a vector are $$A_x = -8$$ units and $$A_y = 6$$ units, what angle does this vector make with the positive x-axis?

$$\theta = \arctan\left(\frac{6}{-8}\right) = 143.1^\circ$$

Q: A force $$F$$ has a magnitude of 25.0 N and points at an angle of $$30^\circ$$ north of east. Take positive x to be east, and positive y to be north. What is the y-component of this force?

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

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 down a straight road at 15 m/s. To overtake a slower vehicle, the driver steps on the accelerator and achieves a constant acceleration of 2.0 m/s$$^2. $$After 5.0 s, the car reaches 25 m/s. How far does the car travel during this period of acceleration?

Accepted Answer

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

Question 3

If the components of a vector are $$A_x = -8$$ units and $$A_y = 6$$ units, what angle does this vector make with the positive x-axis?

Accepted Answer

$$	heta = \arctan\left(\frac{6}{-8}ight) = 143.1^\circ$$

Question 4

Which statement about acceleration is correct?

Accepted Answer

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

Question 5

A cheetah is sprinting in a straight line at 20.0 m/s. It slows down to a stop in 5.00 s. How far does the cheetah travel while decelerating?

Accepted Answer

$$x = v_0$ t + \frac{1}{2} a t^2$, with a$$ = -\frac{$$v_0$$}{t} = -4.0$$ m/s^2$, so x = 20$$ 	imes 5 + \frac{1}{2} 	imes (-4) 	imes 25 = 100 - 50 = 50$$ m

Question 6

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

Accepted Answer

No, the second term $$2a/t^2$$ does not have dimensions of length.

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

It is zero.

Question 9

A force $$F$$ has a magnitude of 25.0 N and points at an angle of $$30^\circ$$ north of east. Take positive x to be east, and positive y to be north. What is the y-component of this force?

Accepted Answer

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

Question 10

If a vector's components are all negative, then the magnitude of the vector is:

Accepted Answer

Positive

Question 11

A brick starts running from rest and accelerates along a straight path. It covers 2.0 m in the first second. Where will it be after 5 seconds?

Accepted Answer

Since $$x = \frac{1}{2} a t^2$, 2.0$$ = \frac{1}{2} a $$(1)^2$$ \Rightarrow a = 4.0$$ m/s^2$. After 5 s: x$$ = \frac{1}{2} 	imes 4.0 	imes 25 = 50$$ m.

Question 12

Which velocity-time graph corresponds to 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 13

When an object moving to the left with a velocity of $$-6 m/s $$west is observed to be gradually coming to rest, what can you conclude about the direction of its acceleration?

Accepted Answer

Acceleration is positive (east) until it stops, then negative.

Question 14

How many significant figures are in the number 0.040?

Accepted Answer

2

Question 15

Given the operation $$\frac{72.0 - 15.60}{0.982 + 4.3}$$, what is the result with the correct number of significant figures?

Accepted Answer

11.6

Question 16

Which of the following is NOT a base SI unit?

Accepted Answer

Newton

Question 17

Which of the following is dimensionally equivalent to acceleration?

Accepted Answer

$$L/T^2$$

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

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