Q: A car starts from rest and accelerates at a constant rate of $$2.5\ \mathrm{m/s^2$}$$ for $$6.0\ \mathrm{s}. $$What is the final velocity of the car?

$$v = 2.5\ \mathrm{m/s^2$} \times 6.0\ \mathrm{s} = 15.0\ \mathrm{m/s}$$

Q: A ball is thrown vertically upward with an initial velocity of $$10.0\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{(10.0)^2$}{2 \times 9.80} = 5.10\ \mathrm{m}$$

Q: A stone is dropped from rest from a tall building. After $$3.00\ \mathrm{s} of $$free fall, what is its displacement? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

$$\Delta y = -\frac{1}{2} g t^2$ = -\frac{1}{2} \times 9.80 \times (3.00)^2$ = -44.1\ \mathrm{m}$$

Q: A jet starts from rest and accelerates down a runway at $$+3.1\ \mathrm{m/s^2$}$$ until it reaches a velocity of $$62\ \mathrm{m/s}. $$How far does it travel during this acceleration?

$$x = \frac{v^2$ - v_0$^2}{2a} = \frac{(62)^2$ - 0^2$}{2 \times 3.1} = 620\ \mathrm{m}$$

Question 1

A car starts from rest and accelerates at a constant rate of $$2.5\ \mathrm{m/s^2$}$$ for $$6.0\ \mathrm{s}. $$What is the final velocity of the car?

Accepted Answer

$$v = 2.5\ \mathrm{m/s^2$} 	imes 6.0\ \mathrm{s} = 15.0\ \mathrm{m/s}$$

Question 2

Which of the following statements is TRUE about an object that is slowing down (decelerating) in one dimension?

Accepted Answer

The velocity and acceleration vectors have opposite directions.

Question 3

A ball is thrown vertically upward with an initial velocity of $$10.0\ \mathrm{m/s}. $$Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{(10.0)^2$}{2 	imes 9.80} = 5.10\ \mathrm{m}$$

Question 4

Which kinematic equation would you use to find the displacement of an object given its initial velocity, acceleration, and time?

Accepted Answer

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

Question 5

A stone is dropped from rest from a tall building. After $$3.00\ \mathrm{s} of $$free fall, what is its displacement? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta y = -\frac{1}{2} g t^2$ = -\frac{1}{2} 	imes 9.80 	imes (3.00)^2$ = -44.1\ \mathrm{m}$$

Question 6

Which of the following is the correct dimensional analysis for the equation $$v = v_0$ + a t$$?

Accepted Answer

[$$L T$$^{-1}$$] = [L$$ $$T^{-1}$$] + [$$L T$$^{-2}$$][T$]

Question 7

A jet starts from rest and accelerates down a runway at $$+3.1\ \mathrm{m/s^2$}$$ until it reaches a velocity of $$62\ \mathrm{m/s}. $$How far does it travel during this acceleration?

Accepted Answer

$$x = \frac{v^2$ - v_0$^2}{2a} = \frac{(62)^2$ - 0^2$}{2 	imes 3.1} = 620\ \mathrm{m}$$

Question 8

If the velocity and acceleration vectors of an object point in the same direction, what happens to the object's speed?

Accepted Answer

The object speeds up.

Question 9

Which of the following is the correct value and direction for the acceleration due to gravity near Earth's surface?

Accepted Answer

$$g = 9.80\ \mathrm{m/s^2$}$$, always points downward

Question 10

A runner accelerates from $$4.0\ \mathrm{m/s} to$$ $$8.0\ \mathrm{m/s} in$$ $$2.0\ \mathrm{s}. $$What is the runner's average acceleration?

Accepted Answer

$$a = \frac{8.0 - 4.0}{2.0} = 2.0\ \mathrm{m/s^2$}$$

Question 11

Which of the following is NOT a recommended step in the general strategy for solving kinematics problems?

Accepted Answer

Plug in numerical values at the very beginning.

Question 12

A ball is thrown downward with an initial velocity of $$5.0\ \mathrm{m/s}$$ from a height of $$20.0\ \mathrm{m}. $$How long does it take to reach the ground? (Use $$g = 9.80\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \frac{-5.0 + \sqrt{(5.0)^2$ + 2 	imes 9.80 	imes 20.0}}{9.80} \approx 1.53\ \mathrm{s}$$

Question 13

Which of the following equations is dimensionally consistent for displacement $$x in $$terms of velocity $$v$$ and time $$t$$?

Accepted Answer

$$x = v t$$

Question 14

A cyclist travels at $$12\ \mathrm{m/s}$$ for $$5.0\ \mathrm{s}$$, then accelerates at $$2.0\ \mathrm{m/s^2$}$$ for $$3.0\ \mathrm{s}. $$What is the total distance covered?

Accepted Answer

$$d = 12 	imes 5.0 + 12 	imes 3.0 + \frac{1}{2} 	imes 2.0 	imes (3.0)^2$ = 60 + 36 + 9 = 105\ \mathrm{m}$$

Question 15

Which of the following is a correct statement about free fall near Earth's surface?

Accepted Answer

All objects fall with the same constant acceleration, regardless of mass, if air resistance is neglected.

Question 16

A ball is thrown upward with an initial velocity $$v_0. At $$its highest point, what is its velocity and acceleration?

Accepted Answer

Velocity is $$0$$, acceleration is $$-g$$

Question 17

Which of the following is the correct kinematic equation for velocity as a function of time under constant acceleration?

Accepted Answer

$$v = v_0$ + a t$$

Question 18

A car moving at $$20\ \mathrm{m/s}$$ comes to a stop in $$4.0\ \mathrm{s}$$ with constant acceleration. What is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{0 - 20}{4.0} = -5.0\ \mathrm{m/s^2$}$$

Kinematics: Motion at Constant Acceleration and Free Fall

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드