Question

acceleration vocabulary
use the following to fill in the blanks

acceleration	direction	meters per second squared (m/s²)	slowing down
velocity	increasing speed	positive	time interval
	negative	seconds	change

speed is the rate of motion of an object. ________________ describes an object’s speed and direction. the velocity of an object can ______________ even if the speed of the object remains constant. this would occur if the ________________ of the object’s motion changes.
the rate of change of velocity is called ________________ . the size of an acceleration depends on both the change in velocity and the ______________ of the change. to calculate acceleration, ______________ the change in velocity by the time interval. to find the change in velocity, ______________ the initial velocity (vᵢ) from the final velocity (vբ). the equation for average acceleration is ______________ . final velocity will be less than initial velocity if an object is ______________ , and acceleration will have a ______________ value. final velocity will be greater than initial velocity if an object is ______________ , and acceleration will have a ________________ value.
the units for velocity are ________________ . the unit for time is ______________ . therefore, the units for acceleration are ________________ .
solve the following (show your work):

1. maddix drives a car that is uniformly accelerated at the rate of 2.5m/s² for 12s. if the original speed of the car is 8.0m/s, what is its final velocity?
2. jesse is in a car whose velocity increases from rest to 14 m/s, in 3.5 sec. what is its acceleration? what is its acceleration if it next slows down to 7 m/s, in 2 sec?
3. emily is in a car that is moving at 16.67 m/s when it begins to decelerate at 1.5m/s². how long does it take for it to slow down to 8.7 m/s?

Explanation:

Step1: Identify the formula for final - velocity

The formula for final velocity in uniformly - accelerated motion is $v = v_0+at$, where $v$ is the final velocity, $v_0$ is the initial velocity, $a$ is the acceleration, and $t$ is the time.

Step2: Substitute the given values into the formula for Maddix's car

Given $v_0 = 8.0m/s$, $a = 2.5m/s^2$, and $t = 12s$.
$v=8.0 + 2.5\times12$
$v=8.0+30$
$v = 38m/s$

Step3: Identify the formula for acceleration

The formula for acceleration is $a=\frac{v - v_0}{t}$, where $v$ is the final velocity, $v_0$ is the initial velocity, and $t$ is the time.

Step4: Calculate the acceleration for Jesse's car when accelerating

Given $v_0 = 0m/s$ (starts from rest), $v = 14m/s$, and $t = 3.5s$.
$a=\frac{14 - 0}{3.5}=\frac{14}{3.5}=4m/s^2$

Step5: Calculate the acceleration for Jesse's car when decelerating

Given $v_0 = 14m/s$, $v = 7m/s$, and $t = 2s$.
$a=\frac{7 - 14}{2}=\frac{- 7}{2}=-3.5m/s^2$

Step6: Rearrange the acceleration formula to solve for time when decelerating

The formula $a=\frac{v - v_0}{t}$ can be rearranged to $t=\frac{v - v_0}{a}$.
For Emily's car, $v_0 = 16.67m/s$, $v = 8.7m/s$, and $a=-1.5m/s^2$ (negative because it's decelerating).
$t=\frac{8.7 - 16.67}{-1.5}=\frac{-7.97}{-1.5}\approx5.31s$

Answer:

1. The final velocity of Maddix's car is $38m/s$.
2. The acceleration of Jesse's car when accelerating is $4m/s^2$ and when decelerating is $-3.5m/s^2$.
3. It takes approximately $5.31s$ for Emily's car to slow down.