Q: A car travels 150 km north in 3 hours, then 150 km south in 2 hours. What is the car's average speed for the entire trip?

$$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{150\,\text{km} + 150\,\text{km}}{3\,\text{h} + 2\,\text{h}} = \frac{300\,\text{km}}{5\,\text{h}} = 60\,\text{km/h}$$

Q: A ball is dropped from rest from a tall building. Ignoring air resistance, what is its velocity after 3 seconds? (Take $$g = 10\,\text{m/s}^2)$$

$$v = g t = 10\,\text{m/s}^2 \times 3\,\text{s} = 30\,\text{m/s}$$

Q: A runner completes one lap around a 400 m track in 100 seconds, ending at the starting point. What is the runner's average velocity?

$$\text{Average velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{0\,\text{m}}{100\,\text{s}} = 0\,\text{m/s}$$

Q: A car accelerates from rest to $$20\,\text{m/s} in$$ $$5\,\text{s}. $$What is its acceleration?

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

Q: A stone is thrown vertically upward with an initial speed of $$20\,\text{m/s}. $$How long does it take to reach its highest point? (Take $$g = 10\,\text{m/s}^2)$$

$$t = \frac{v}{g} = \frac{20\,\text{m/s}}{10\,\text{m/s}^2} = 2\,\text{s}$$

Q: A freely falling object starts from rest. What is the distance it falls after 3 seconds? (Take $$g = 10\,\text{m/s}^2)$$

$$d = \frac{1}{2} g t^2$ = \frac{1}{2} \times 10\,\text{m/s}^2 \times (3\,\text{s})^2$ = 45\,\text{m}$$

Question 1

A car travels 150 km north in 3 hours, then 150 km south in 2 hours. What is the car's average speed for the entire trip?

Accepted Answer

$$	ext{Average speed} = \frac{	ext{Total distance}}{	ext{Total time}} = \frac{150\,	ext{km} + 150\,	ext{km}}{3\,	ext{h} + 2\,	ext{h}} = \frac{300\,	ext{km}}{5\,	ext{h}} = 60\,	ext{km/h}$$

Question 2

Which of the following statements best describes velocity?

Accepted Answer

Velocity is a vector quantity describing both the speed and direction of an object.

Question 3

A ball is dropped from rest from a tall building. Ignoring air resistance, what is its velocity after 3 seconds? (Take $$g = 10\,	ext{m/s}^2)$$

Accepted Answer

$$v = g t = 10\,	ext{m/s}^2 	imes 3\,	ext{s} = 30\,	ext{m/s}$$

Question 4

A runner completes one lap around a 400 m track in 100 seconds, ending at the starting point. What is the runner's average velocity?

Accepted Answer

$$	ext{Average velocity} = \frac{	ext{Displacement}}{	ext{Time}} = \frac{0\,	ext{m}}{100\,	ext{s}} = 0\,	ext{m/s}$$

Question 5

A car accelerates from rest to $$20\,	ext{m/s} in$$ $$5\,	ext{s}. $$What is its acceleration?

Accepted Answer

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

Question 6

Which of the following scenarios describes an object that is accelerating?

Accepted Answer

Both slowing down to a stop and rounding a curve at a steady speed.

Question 7

A stone is thrown vertically upward with an initial speed of $$20\,	ext{m/s}. $$How long does it take to reach its highest point? (Take $$g = 10\,	ext{m/s}^2)$$

Accepted Answer

$$t = \frac{v}{g} = \frac{20\,	ext{m/s}}{10\,	ext{m/s}^2} = 2\,	ext{s}$$

Question 8

A freely falling object starts from rest. What is the distance it falls after 3 seconds? (Take $$g = 10\,	ext{m/s}^2)$$

Accepted Answer

$$d = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 10\,	ext{m/s}^2 	imes (3\,	ext{s})^2$ = 45\,	ext{m}$$

Question 9

A plane is flying north at $$80\,	ext{km/h}$$ and encounters a crosswind blowing east at $$60\,	ext{km/h}. $$What is the plane's resultant speed?

Accepted Answer

$$v = \sqrt{80^2$ + 60^2$} = \sqrt{6400 + 3600} = \sqrt{10000} = 100\,	ext{km/h}$$

Question 10

You run horizontally at $$4\,	ext{m/s} in a $$vertically falling rain that falls at $$4\,	ext{m/s}. $$Relative to you, at what angle from the vertical do the raindrops appear to fall?

Accepted Answer

$$45^\circ$$

Question 11

A cyclist travels 30 km in 1 hour. Which of the following trips would result in the same average speed?

Accepted Answer

60 km in 2 hours

Question 12

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

Accepted Answer

Speed is a scalar; velocity is a vector.

Question 13

A car's speed increases from $$10\,	ext{m/s} to$$ $$30\,	ext{m/s} in$$ $$4\,	ext{s}. $$What is its acceleration?

Accepted Answer

$$a = \frac{30\,	ext{m/s} - 10\,	ext{m/s}}{4\,	ext{s}} = 5\,	ext{m/s}^2$$

Question 14

A ball is thrown straight up with an initial velocity of $$15\,	ext{m/s}. $$What is its velocity after 2 seconds? (Take $$g = 10\,	ext{m/s}^2)$$

Accepted Answer

$$v = 15\,	ext{m/s} - 10\,	ext{m/s}^2 	imes 2\,	ext{s} = -5\,	ext{m/s}$$

Question 15

Which of the following is true about acceleration and velocity?

Accepted Answer

Both are rates, but for different quantities.

Question 16

A rock is dropped from a cliff and falls freely for 4 seconds. What is the distance it falls? (Take $$g = 10\,	ext{m/s}^2)$$

Accepted Answer

$$d = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 10 	imes 16 = 80\,	ext{m}$$

Question 17

A car moves at a constant velocity. Which of the following must be true?

Accepted Answer

The car moves in a straight line at constant speed.

Question 18

A skydiver jumps from a plane and falls freely before opening the parachute. What is the acceleration during free fall (ignoring air resistance)?

Accepted Answer

$$a = 9.8\,	ext{m/s}^2$$

Linear Motion: Physics with Calculus Study Notes

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