Q: A car travels 120 km north in 2 hours, then 80 km south in 1 hour. What is the car's average velocity for the entire trip?

$$\frac{120\,\text{km} - 80\,\text{km}}{3\,\text{h}} = \frac{40\,\text{km}}{3\,\text{h}} = 13.3\,\text{km/h}$$\, north

Q: A ball is thrown vertically upward with an initial velocity of $$15\,\text{m/s}. $$What is the maximum height it reaches? (Assume $$g = 9.8\,\text{m/s}^2)$$

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 \times 9.8} = \frac{225}{19.6} = 11.5\,\text{m}$$

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

$$v = v_0$ + at = 0 + 2 \times 5 = 10\,\text{m/s}$$

Q: A cyclist moves at a constant velocity of $$10\,\text{m/s}$$ for $$30\,\text{s}. $$What is the total displacement?

$$d = v t = 10 \times 30 = 300\,\text{m}$$

Q: A student drops a ball from a height of $$2\,\text{m}. $$What is the speed of the ball just before it hits the ground? (Assume $$g = 9.8\,\text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} = \sqrt{39.2} = 6.26\,\text{m/s}$$

Question 1

A car travels 120 km north in 2 hours, then 80 km south in 1 hour. What is the car's average velocity for the entire trip?

Accepted Answer

$$\frac{120\,	ext{km} - 80\,	ext{km}}{3\,	ext{h}} = \frac{40\,	ext{km}}{3\,	ext{h}} = 13.3\,	ext{km/h}$$\, north

Question 2

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

Accepted Answer

Velocity includes direction, while speed does not.

Question 3

A ball is thrown vertically upward with an initial velocity of $$15\,	ext{m/s}. $$What is the maximum height it reaches? (Assume $$g = 9.8\,	ext{m/s}^2)$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(15)^2$}{2 	imes 9.8} = \frac{225}{19.6} = 11.5\,	ext{m}$$

Question 4

Which of the following is NOT a vector quantity?

Accepted Answer

Speed

Question 5

A runner accelerates from rest at $$2\,	ext{m/s}^2$$ for $$5\,	ext{s}. $$What is the runner's final velocity?

Accepted Answer

$$v = v_0$ + at = 0 + 2 	imes 5 = 10\,	ext{m/s}$$

Question 6

A projectile is launched horizontally from a $$20\,	ext{m}$$ high cliff with a speed of $$5\,	ext{m/s}. $$How long does it take to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} = \sqrt{4.08} = 2.02\,	ext{s}$$

Question 7

Which kinematic equation is best suited to solve for displacement when acceleration is constant and initial and final velocities are known?

Accepted Answer

$$v^2$$ = $$v_0^2 + 2a(x$$ - $$x_0$$)$$

Question 8

A cyclist moves at a constant velocity of $$10\,	ext{m/s}$$ for $$30\,	ext{s}. $$What is the total displacement?

Accepted Answer

$$d = v t = 10 	imes 30 = 300\,	ext{m}$$

Question 9

A student drops a ball from a height of $$2\,	ext{m}. $$What is the speed of the ball just before it hits the ground? (Assume $$g = 9.8\,	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} = \sqrt{39.2} = 6.26\,	ext{m/s}$$

Question 10

Which of the following best describes the motion of a projectile?

Accepted Answer

It moves with constant horizontal velocity and constant vertical acceleration.

Question 11

A car starts from rest and accelerates at $$3\,	ext{m/s}^2$$ for $$4\,	ext{s}. $$What is the total displacement?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + \frac{1}{2} 	imes 3 	imes 16 = 24\,	ext{m}$$

Question 12

Which of the following is a correct unit conversion for $$5\,	ext{km} to $$meters?

Accepted Answer

$$5\,	ext{km} = 5000\,	ext{m}$$

Question 13

A position vs time plot for an object shows a straight line with positive slope. What does this indicate about the object's motion?

Accepted Answer

The object is moving at constant velocity.

Question 14

A velocity vs time plot for an object shows a horizontal line at $$v = 0. $$What does this indicate?

Accepted Answer

The object is at rest.

Question 15

A projectile is launched at an angle of $$30^\circ$$ with an initial speed of $$20\,	ext{m/s}. $$What is the initial vertical component of its velocity?

Accepted Answer

$$v_{y0} = v_0$ \sin 	heta = 20 \sin 30^\circ = 10\,	ext{m/s}$$

Question 16

Which of the following best describes instantaneous velocity?

Accepted Answer

The velocity at a specific moment in time.

Question 17

A car moves east at $$15\,	ext{m/s}$$ for $$10\,	ext{s}$$, then west at $$10\,	ext{m/s}$$ for $$5\,	ext{s}. $$What is the car's total displacement?

Accepted Answer

$$d = 15 	imes 10 - 10 	imes 5 = 150 - 50 = 100\,	ext{m}$$\, east

Question 18

A student throws a rock horizontally from a bridge $$10\,	ext{m}$$ above a river. If the rock lands $$8\,	ext{m}$$ from the base of the bridge, what was the initial speed of the rock? (Assume $$g = 9.8\,	ext{m/s}^2)$$

Accepted Answer

$$v_0$$ = \frac{d}{t}$$, where t$$ = \sqrt{\frac{2h}{g}} = \sqrt{\frac{20}{9.8}} = 1.43\,	ext{s}$$, so v_0$ = \frac{8}{1.43} = 5.6\,	ext{m/s}$$

PHYS 210 Exam 1 Study Guide: Kinematics and Motion

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