Q: A car travels 120 m east and then 300 m north. What is the magnitude of its displacement?

$$\sqrt{120^2$ + 300^2$} = 323.1\ \text{m}$$

Q: Given the position vector $$\vec{r} = x\hat{i} + y\hat{j}$$, what is the angle $$\theta it $$makes with the x-axis?

$$\theta = \tan$$^{-1}$$\left(\frac{y}{x}\right)$$

Q: A car moves with a velocity of $$20\ \text{m/s}$$ for $$10\ \text{s}$$, then stops in $$5\ \text{s}$$ with constant acceleration. What is the acceleration during stopping?

$$a = \frac{0 - 20}{5} = -4\ \text{m/s}^2$$

Q: A boat moves north at $$10\ \text{m/s}$$ relative to the water, while the river flows east at $$3\ \text{m/s}. $$What is the boat's speed relative to the ground?

$$\sqrt{10^2$ + 3^2$} = 10.44\ \text{m/s}$$

Q: A cyclist travels 60 km north in 2 hours, then 80 km east in 4 hours. What is the average speed for the entire trip?

$$\frac{60 + 80}{2 + 4} = 23.3\ \text{km/h}$$

Q: A car accelerates from rest at $$2\ \text{m/s}^2$$ for $$5\ \text{s}. $$What is its final velocity?

$$v = 0 + 2 \times 5 = 10\ \text{m/s}$$

Question 1

A car travels 120 m east and then 300 m north. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{120^2$ + 300^2$} = 323.1\ 	ext{m}$$

Question 2

Which of the following best describes the difference between distance and displacement?

Accepted Answer

Distance is the total length of the path traveled, while displacement is the straight-line vector from start to finish.

Question 3

A runner completes one lap around a 400 m circular track in 80 s. What is the runner's average velocity?

Accepted Answer

$$0\ 	ext{m/s}$$

Question 4

Given the position vector $$\vec{r} = x\hat{i} + y\hat{j}$$, what is the angle $$	heta it $$makes with the x-axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{y}{x}ight)$$

Question 5

A car moves with a velocity of $$20\ 	ext{m/s}$$ for $$10\ 	ext{s}$$, then stops in $$5\ 	ext{s}$$ with constant acceleration. What is the acceleration during stopping?

Accepted Answer

$$a = \frac{0 - 20}{5} = -4\ 	ext{m/s}^2$$

Question 6

Which of the following statements about instantaneous velocity is correct?

Accepted Answer

It is the derivative of position with respect to time: $$\vec{v} = \frac{d\vec{r}}{dt}$$

Question 7

A boat moves north at $$10\ 	ext{m/s}$$ relative to the water, while the river flows east at $$3\ 	ext{m/s}. $$What is the boat's speed relative to the ground?

Accepted Answer

$$\sqrt{10^2$ + 3^2$} = 10.44\ 	ext{m/s}$$

Question 8

If the velocity-time graph of a car is a straight line with a positive slope, what does this indicate?

Accepted Answer

The car is accelerating at a constant rate.

Question 9

A truck moves at $$100\ 	ext{m/s}$$ east relative to the ground, and a car moves at $$150\ 	ext{m/s}$$ east relative to the ground. What is the velocity of the truck relative to the car?

Accepted Answer

$$-50\ 	ext{m/s}$$

Question 10

Which of the following is true about inertial frames of reference?

Accepted Answer

They are not accelerating.

Question 11

A cyclist travels 60 km north in 2 hours, then 80 km east in 4 hours. What is the average speed for the entire trip?

Accepted Answer

$$\frac{60 + 80}{2 + 4} = 23.3\ 	ext{km/h}$$

Question 12

The area under a velocity-time graph represents:

Accepted Answer

Displacement

Question 13

A car accelerates from rest at $$2\ 	ext{m/s}^2$$ for $$5\ 	ext{s}. $$What is its final velocity?

Accepted Answer

$$v = 0 + 2 	imes 5 = 10\ 	ext{m/s}$$

Question 14

Which of the following is the correct formula for average velocity?

Accepted Answer

$$\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}$$

Question 15

A bus moves at $$5\ 	ext{m/s}$$ east relative to the ground. A passenger walks at $$1\ 	ext{m/s}$$ east relative to the bus. What is the passenger's velocity relative to the ground?

Accepted Answer

$$6\ 	ext{m/s}$$ east

Question 16

If a velocity-time graph is a horizontal line above the time axis, what does this indicate?

Accepted Answer

The object is moving at constant velocity.

Question 17

A car travels 100 km at 50 km/h and then another 100 km at 100 km/h. What is the average speed for the entire trip?

Accepted Answer

$$\frac{200}{2 + 1} = 66.7\ 	ext{km/h}$$

Question 18

Which of the following is the correct expression for instantaneous acceleration?

Accepted Answer

$$\vec{a} = \frac{d\vec{v}}{dt}$$

Question 19

A car is moving at $$20\ 	ext{m/s}$$ and slows down to $$5\ 	ext{m/s} in$$ $$3\ 	ext{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{5 - 20}{3} = -5\ 	ext{m/s}^2$$

Kinematics: Describing Motion in One and Two Dimensions

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