Q: A car moves with a constant velocity of $$15\ \mathrm{m/s}$$ along a straight road. If its initial position is $$x_0 = 10$$\ \mathrm{m}$$ at t_0$ = 0$$, what is its position after $$8\ \mathrm{s}$$?

$$x = x_0$ + v t = 10 + 15 \times 8 = 130\ \mathrm{m}$$

Q: A truck accelerates from rest at $$a = 2.5\ \mathrm{m/s^2$}$$ for $$6\ \mathrm{s}. $$What is its final velocity?

$$v = v_0$ + a t = 0 + 2.5 \times 6 = 15\ \mathrm{m/s}$$

Q: A cyclist rides off a $$6.0\ \mathrm{m}$$ high cliff with a horizontal velocity of $$20.0\ \mathrm{m/s}. $$How far from the base of the cliff will the cyclist land? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 6.0}{9.8}} = 1.11\ \mathrm{s}$$, $$R = v_{0x} t = 20.0 \times 1.11 = 22.2\ \mathrm{m}$$

Q: A projectile is launched horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 45}{9.8}} = 3.03\ \mathrm{s}$$

Question 1

A car moves with a constant velocity of $$15\ \mathrm{m/s}$$ along a straight road. If its initial position is $$x_0 = 10$$\ \mathrm{m}$$ at t_0$ = 0$$, what is its position after $$8\ \mathrm{s}$$?

Accepted Answer

$$x = x_0$ + v t = 10 + 15 	imes 8 = 130\ \mathrm{m}$$

Question 2

A truck accelerates from rest at $$a = 2.5\ \mathrm{m/s^2$}$$ for $$6\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = v_0$ + a t = 0 + 2.5 	imes 6 = 15\ \mathrm{m/s}$$

Question 3

A projectile is launched from the ground with an initial speed of $$40\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the maximum height it reaches? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$y_{max} = \frac{v_{0y}^2}{2g} = \frac{(40 \sin 30^\$$circ)^2$$}{2 	imes 9.8} = \frac{(20)^2$}{19.6} = 20.4\ \mathrm{m}$$

Question 4

A cyclist rides off a $$6.0\ \mathrm{m}$$ high cliff with a horizontal velocity of $$20.0\ \mathrm{m/s}. $$How far from the base of the cliff will the cyclist land? (Ignore air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 6.0}{9.8}} = 1.11\ \mathrm{s}$$, $$R = v_{0x} t = 20.0 	imes 1.11 = 22.2\ \mathrm{m}$$

Question 5

Which of the following best describes the motion of a projectile launched at an angle $$\$$theta_0$$ with initial speed v_0$ (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity changes due to gravity.

Question 6

A ball is thrown vertically upward with an initial velocity of $$25\ \mathrm{m/s}. $$How long does it take to reach its maximum height? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t_{max} = \frac{v_0$}{g} = \frac{25}{9.8} = 2.55\ \mathrm{s}$$

Question 7

A rocket is launched at $$60^\circ$$ above the horizontal with an initial speed of $$50\ \mathrm{m/s}. $$What is the total time the rocket spends in the air? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t_{flight} = \frac{2 v_0$ \sin \$$theta_0$$}{g} = \frac{2 	imes 50 	imes \sin 60^\circ}{9.8} = \frac{2 	imes 50 	imes 0.866}{9.8} = 8.83\ \mathrm{s}$$

Question 8

A position vs. time graph for an object shows a curve that gets steeper as time increases. What does this indicate about the object's motion?

Accepted Answer

The object is accelerating.

Question 9

A car starts from rest and accelerates uniformly at $$3.0\ \mathrm{m/s^2$}$$ for $$5.0\ \mathrm{s}. $$What distance does it cover in this time?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$ = 0 + 0 + \frac{1}{2} 	imes 3.0 	imes 25 = 37.5\ \mathrm{m}$$

Question 10

A projectile is launched horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 45}{9.8}} = 3.03\ \mathrm{s}$$

Question 11

A ball is dropped from a height $$h$$ and hits the ground after $$t$$ seconds. Which equation correctly relates $$h$$, $$g$$, and $$t$$?

Accepted Answer

$$h = \frac{1}{2} g t^2$

Question 12

A projectile is launched from the ground with initial speed $$v_0 at $$angle $$\$$theta_0$$. What is the formula for its range R$ (horizontal distance traveled before landing)?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2\$$theta_0$$}{g}$$

Question 13

A car moves with a constant velocity. Which of the following statements is true?

Accepted Answer

The net force acting on the car is zero.

Question 14

A stone is thrown downward from a cliff with an initial velocity of $$5\ \mathrm{m/s}. $$How far does it fall in $$3\ \mathrm{s}$$? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$y = v_0$ t + \frac{1}{2} g t^2$ = 5 	imes 3 + 0.5 	imes 9.8 	imes 9 = 15 + 44.1 = 59.1\ \mathrm{m}$$

Question 15

A ball is thrown horizontally from a $$20\ \mathrm{m}$$ high tower with a speed of $$10\ \mathrm{m/s}. $$What is the horizontal distance it travels before hitting the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{40}{9.8}} = 2.02\ \mathrm{s}$$, $$R = v_{0x} t = 10 	imes 2.02 = 20.2\ \mathrm{m}$$

Question 16

Which of the following is the correct kinematic equation for position under constant acceleration?

Accepted Answer

$$x = x_0$ + v_0$ t + \frac{1}{2} a t^2$

Question 17

A projectile is launched from a height $$y_0$$ above the ground with initial vertical velocity $$v_{0y}. $$What is the time $$t it $$takes to hit the ground?

Accepted Answer

$$y = y_0$ + v_{0y} t - \frac{1}{2} g t^2$ = 0$$

Kinematics: Motion in One and Two Dimensions

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