Question

1. in your own words explain what a \positive\ or

egative\ velocity means. what does the sign (+ or -) tell you about the velocity?

1. true or false: if an object has a negative velocity and a positive acceleration it is slowing down. explain your reasoning.
2. true or false: if an object has a positive velocity and a positive acceleration it is speeding up. explain your reasoning.
3. a car has an initial velocity of 30 meters per second. it applies its brakes causing it to have a negative acceleration of -0.6 m/s². how long will it take the car to come to a stop? (hint: use the kinematic equation you learned. what must the final velocity be when the car has come to a stop?)
4. a train starts from rest and has an acceleration of 1.5 m/s². after 30 seconds, what is the velocity of the train?
5. a wakeboarder has an initial velocity of 10 m/s. she puts her foot in the sand slightly, causing her to slow down with some unknown, constant acceleration. if she comes to a stop after 5 seconds, what must have been her acceleration?
6. a skateboarder starts up a ramp with an initial velocity of 8 m/s. he experiences a constant acceleration of - 4 m/s².

a. how long will it take the skateboarder to come to a stop?
b. what will be his velocity after 1 second?
c. what will be his velocity after 2 seconds?
d. what will be his velocity after 4 seconds?

1. in your own words, describe what acceleration is and how it relates to velocity.
2. neatly copy the chart below and fill in the blanks. use the internet if you are unsure what the metric prefix is. please note that there are more metric prefixes. these are just some commonly used prefixes. \float\ notation means writing a number out like this \0.001\. that same number expressed as a power of ten would be 10⁻³.

metric prefix symbol multiplier floating notation multiplier power of ten
giga 10⁹
mega 1,000,000
kilo k
d 10⁻¹
centi
milli 0.001
μ 10⁻⁶
nano

Explanation:

Step1: Define positive and negative velocity

Positive velocity means the object is moving in the chosen positive - direction. Negative velocity means the object is moving in the opposite (negative) direction. The sign indicates the direction of motion relative to a chosen coordinate system.

Step2: Answer question 2

False. If an object has a negative velocity and positive acceleration, the acceleration is acting to slow down the negative - velocity (opposite to the direction of motion initially), but it will eventually reverse the direction and speed up in the positive direction. For example, a car moving backwards (negative velocity) and braking (positive acceleration relative to the forward direction).

Step3: Answer question 3

True. When an object has a positive velocity and positive acceleration, the acceleration is in the same direction as the velocity, so it speeds up. For example, a car moving forward (positive velocity) and accelerating forward (positive acceleration).

Step4: Solve question 4

We use the kinematic equation $v = v_0+at$, where $v = 0$ (final velocity when stopped), $v_0 = 30\ m/s$, and $a=- 0.6\ m/s^2$.
\[

$$\begin{align*} 0&=30+( - 0.6)t\\ 0.6t&=30\\ t&=\frac{30}{0.6}=50\ s \end{align*}$$

\]
The final velocity when the car has come to a stop is $0\ m/s$.

Step5: Solve question 5

Using the kinematic equation $v = v_0+at$, with $v_0 = 0$ (starts from rest), $a = 1.5\ m/s^2$, and $t = 30\ s$.
\[
v=0 + 1.5\times30=45\ m/s
\]

Step6: Solve question 6

Using the kinematic equation $v = v_0+at$, with $v = 0$ (comes to a stop), $v_0 = 10\ m/s$, and $t = 5\ s$.
\[

$$\begin{align*} 0&=10+a\times5\\ 5a&=-10\\ a&=- 2\ m/s^2 \end{align*}$$

\]

Step7: Solve question 7a

Using the kinematic equation $v = v_0+at$, with $v = 0$ (comes to a stop), $v_0 = 8\ m/s$, and $a=-4\ m/s^2$.
\[

$$\begin{align*} 0&=8+( - 4)t\\ 4t&=8\\ t& = 2\ s \end{align*}$$

\]

Step8: Solve question 7b

Using the kinematic equation $v = v_0+at$, with $v_0 = 8\ m/s$, $a=-4\ m/s^2$, and $t = 1\ s$.
\[
v=8+( - 4)\times1=4\ m/s
\]

Step9: Solve question 7c

Using the kinematic equation $v = v_0+at$, with $v_0 = 8\ m/s$, $a=-4\ m/s^2$, and $t = 2\ s$.
\[
v=8+( - 4)\times2=0\ m/s
\]

Step10: Solve question 7d

Using the kinematic equation $v = v_0+at$, with $v_0 = 8\ m/s$, $a=-4\ m/s^2$, and $t = 4\ s$.
\[
v=8+( - 4)\times4=8 - 16=-8\ m/s
\]

Step11: Define acceleration for question 8

Acceleration is the rate of change of velocity. Mathematically, $a=\frac{\Delta v}{\Delta t}$. If acceleration and velocity are in the same direction, the object speeds up. If they are in opposite directions, the object slows down.

Step12: Fill in the table for question 9

Metric Prefix	Symbol	Multiplier Floating Notation	Multiplier Power of Ten
mega	M	1000000	$10^{6}$
kilo	k	1000	$10^{3}$
deci	d	0.1	$10^{-1}$
centi	c	0.01	$10^{-2}$
milli	m	0.001	$10^{-3}$
micro	$\mu$	0.000001	$10^{-6}$
nano	n	0.000000001	$10^{-9}$

Answer:

1. Positive velocity means motion in the chosen positive - direction; negative velocity means motion in the opposite direction. The sign indicates direction.
2. False. Explanation: Positive acceleration acts against negative velocity, first slowing it down and then reversing direction.
3. True. Explanation: Positive acceleration in the direction of positive velocity speeds up the object.
4. $t = 50\ s$, final velocity $v = 0\ m/s$
5. $v = 45\ m/s$
6. $a=-2\ m/s^2$

7a. $t = 2\ s$
7b. $v = 4\ m/s$
7c. $v = 0\ m/s$
7d. $v=-8\ m/s$

1. Acceleration is the rate of change of velocity. If in same direction as velocity, object speeds up; if opposite, it slows down.
2. See filled - in table above.