Question

acceleration practice worksheet
use the equation: a=(v_f - v_i)/t or equivalently: δv = a×t
show all work, include units, and circle your final answer.
solve for final velocity (v_f)

1. a car starts at a speed of 12 m/s and accelerates at 2.5 m/s² for 6.0 seconds. what is its final velocity?
2. a runner with an initial speed of 4.0 m/s accelerates at 1.2 m/s² for 10 seconds. what is the runner’s final speed?

solve for initial velocity (v_i)

1. a motorcycle accelerates at 3.0 m/s² for 5.0 seconds and reaches a final velocity of 40 m/s. what was its initial velocity?
2. a car accelerates at 2.0 m/s² for 8.0 seconds and ends at 30 m/s. what was its starting velocity?

solve for acceleration (a)

1. a truck goes from 10 m/s to 25 m/s in 3.0 seconds. what is the truck’s acceleration?

Explanation:

Step1: Recall the acceleration - velocity formula

The formula $a=\frac{v_f - v_i}{t}$ can be rewritten as $v_f=v_i + at$.

Step2: Solve problem 1

Given $v_i = 12\ m/s$, $a = 2.5\ m/s^2$, and $t = 6.0\ s$.
$v_f=v_i+at=12 + 2.5\times6=12 + 15=27\ m/s$.

Step3: Solve problem 2

Given $v_i = 4.0\ m/s$, $a = 1.2\ m/s^2$, and $t = 10\ s$.
$v_f=v_i+at=4.0+1.2\times10=4.0 + 12=16\ m/s$.

Step4: Rearrange the formula for initial - velocity

From $a=\frac{v_f - v_i}{t}$, we get $v_i=v_f - at$.

Step5: Solve problem 3

Given $v_f = 40\ m/s$, $a = 3.0\ m/s^2$, and $t = 5.0\ s$.
$v_i=v_f - at=40-3.0\times5=40 - 15=25\ m/s$.

Step6: Solve problem 4

Given $v_f = 30\ m/s$, $a = 2.0\ m/s^2$, and $t = 8.0\ s$.
$v_i=v_f - at=30-2.0\times8=30 - 16=14\ m/s$.

Step7: Solve for acceleration formula

From $a=\frac{v_f - v_i}{t}$.

Step8: Solve problem 5

Given $v_i = 10\ m/s$, $v_f = 25\ m/s$, and $t = 3.0\ s$.
$a=\frac{v_f - v_i}{t}=\frac{25 - 10}{3}=\frac{15}{3}=5\ m/s^2$.

Answer:

1. $27\ m/s$
2. $16\ m/s$
3. $25\ m/s$
4. $14\ m/s$
5. $5\ m/s^2$