Q: Which of the following is the correct definition of instantaneous acceleration?

$$a_x = \lim_{\Delta t \to 0} \frac{\Delta v_x}{\Delta t}$$

Question 1

A car travels in the negative x-direction at 25 m/s and slows down to 10 m/s over a period of 5 seconds, continuing in the negative x-direction. What is the car's average acceleration during this period?

Accepted Answer

$$-3 \, \mathrm{m/s^2$}$$

Question 2

Which of the following statements is TRUE regarding velocity and acceleration?

Accepted Answer

If velocity and acceleration are in the same direction, the object is speeding up.

Question 3

A hiker walks 2.50 km at $$45.0^\circ$$ southeast, then 4.00 km at $$60.0^\circ$$ north of east. What is the best method to find her total displacement from the starting point?

Accepted Answer

Resolve each walk into x and y components, sum the components, then use the Pythagorean theorem.

Question 4

Which equation correctly defines average velocity?

Accepted Answer

$$v_{avg} = \frac{\Delta x}{\Delta t}$$

Question 5

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$5$$

Question 6

Which of the following best describes a unit vector?

Accepted Answer

A vector with magnitude 1 and no units, pointing in a coordinate direction.

Question 7

Given $$\vec{A} = 4\hat{i} + 3\hat{j}$$ and $$\vec{B} = -2\hat{i} + 5\hat{j}$$, what is $$\vec{A} + \vec{B}$$?

Accepted Answer

$$2\hat{i} + 8\hat{j}$$

Question 8

The instantaneous velocity at a given time is found by:

Accepted Answer

The slope of the tangent line to the $$x vs$$. $$t$$ graph at that time.

Question 9

A car's velocity changes from $$10 \, \mathrm{m/s} to$$ $$-20 \, \mathrm{m/s} in$$ $$5$$ seconds. What is its average acceleration?

Accepted Answer

Question 10

Which of the following is NOT a correct statement about displacement?

Accepted Answer

Displacement is always equal to the distance traveled.

Question 11

If a velocity vs. time graph shows a straight line with negative slope, what does this indicate about the object's motion?

Accepted Answer

The object is accelerating in the negative direction.

Question 12

Which formula gives the x-component of a vector $$\vec{A}$$ with magnitude $$A at an $$angle $$	heta$$ from the x-axis?

Accepted Answer

$$A_x = A \cos 	heta$$

Question 13

A train moves along a straight track. Its position vs. time graph is a curve that gets steeper with time. What does this indicate?

Accepted Answer

The train is accelerating.

Question 14

Which of the following is the correct definition of instantaneous acceleration?

Accepted Answer

$$a_x = \lim_{\Delta t 	o 0} \frac{\Delta v_x}{\Delta t}$$

Question 15

A vector $$\vec{C} is $$defined as $$\vec{C} = \vec{A} - \vec{B}$$, where $$\vec{A}$$ and $$\vec{B}$$ both have magnitude $$6.0 m $$and point in opposite directions. What is the magnitude of $$\vec{C}$$?

Accepted Answer

$$12.0 m$$

Question 16

Which of the following is a scalar component of a vector $$\vec{A}$$?

Accepted Answer

$$A_x$$

Question 17

A car's velocity changes from $$-10 \, \mathrm{m/s} to$$ $$-20 \, \mathrm{m/s} in$$ $$5$$ seconds. What is the average acceleration?

Accepted Answer

$$-2 \, \mathrm{m/s^2$}$$

Question 18

Which of the following is true about average speed and average velocity?

Accepted Answer

Average speed is the total distance divided by total time, while average velocity is the total displacement divided by total time.

Vector Addition and Linear Motion: Study Notes for PHY 121 University Physics I - Mechanics

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