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

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