Question

A toy race car zooms across the ground with an acceleration of 2.8 m/s2
. After 4 seconds it has a final velocity of 22.2 m/s, what is the toy car's initial velocity?

**Be sure to show your work and include units for your final answer.**

(3 points)

Answer 1

To find the initial velocity of the toy race car, we can use the formula for final velocity in uniformly accelerated motion:

\[
v_f = v_i + a \cdot t
\]

Where:
- \( v_f \) = final velocity
- \( v_i \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

We are given:
- \( v_f = 22.2 \, \text{m/s} \)
- \( a = 2.8 \, \text{m/s}^2 \)
- \( t = 4 \, \text{s} \)

Rearranging the formula to solve for the initial velocity (\( v_i \)) gives us:

\[
v_i = v_f - a \cdot t
\]

Now, we can substitute the known values into the equation:

\[
v_i = 22.2 \, \text{m/s} - (2.8 \, \text{m/s}^2 \cdot 4 \, \text{s})
\]

Calculating the acceleration term:

\[
a \cdot t = 2.8 \, \text{m/s}^2 \cdot 4 \, \text{s} = 11.2 \, \text{m/s}
\]

Now we can substitute that back into the equation for \( v_i \):

\[
v_i = 22.2 \, \text{m/s} - 11.2 \, \text{m/s}
\]

Doing the arithmetic gives:

\[
v_i = 11.0 \, \text{m/s}
\]

Thus, the initial velocity of the toy race car is

\[
\boxed{11.0 \, \text{m/s}}
\]