Question

use the following to fill in the blanks

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

speed is the rate of motion of an object. describes an objects 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 objects 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 ($v_i$) from the final velocity ($v_f$). 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: Recall the acceleration - velocity formula

The formula for acceleration is $a=\frac{v_f - v_i}{t}$, and we can re - arrange it to find $v_f=v_i + at$.

Step2: Identify the values for Maddix's car

For Maddix's car, $v_i = 8.0\ m/s$, $a = 2.5\ m/s^2$, and $t = 12\ s$.

Step3: Calculate the final velocity

Substitute the values into the formula: $v_f=8.0+2.5\times12$.
$v_f=8.0 + 30=38\ m/s$.

Step4: For Jesse's first acceleration

The initial velocity $v_i = 0\ m/s$ (starts from rest), the final velocity $v_f = 14\ m/s$, and $t = 3.5\ s$. Using the formula $a=\frac{v_f - v_i}{t}$, we have $a=\frac{14 - 0}{3.5}=4\ m/s^2$.

Step5: For Jesse's second acceleration

The initial velocity $v_i = 14\ m/s$, the final velocity $v_f = 7\ m/s$, and $t = 2\ s$. Using the formula $a=\frac{v_f - v_i}{t}$, we get $a=\frac{7 - 14}{2}=- 3.5\ m/s^2$.

Step6: For Emily's car

The initial velocity $v_i = 16.67\ m/s$, the final velocity $v_f = 8.7\ m/s$, and the acceleration $a=-1.5\ m/s^2$ (deceleration). Rearranging the formula $a=\frac{v_f - v_i}{t}$ to solve for $t$, we get $t=\frac{v_f - v_i}{a}$.
$t=\frac{8.7 - 16.67}{-1.5}=\frac{-7.97}{-1.5}\approx5.31\ s$.

Answer:

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