Questions: A sports car accelerates from rest to 80 km/h in 5.0 s. What is its average acceleration in m/s^2? Express your answer using two significant figures.

Solution Steps

The car accelerates from rest to a final velocity of \(80 \, \text{km/h}\). We need to convert this velocity to meters per second (\(\text{m/s}\)).

\[ 80 \, \text{km/h} = 80 \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = \frac{80000}{3600} \, \text{m/s} \approx 22.2222 \, \text{m/s} \]

The average acceleration (\(a\)) is given by the change in velocity (\(\Delta v\)) divided by the time (\(t\)) it takes for that change. The initial velocity (\(v_0\)) is \(0 \, \text{m/s}\) since the car starts from rest.

\[ a = \frac{\Delta v}{t} = \frac{v - v_0}{t} = \frac{22.2222 \, \text{m/s} - 0 \, \text{m/s}}{5.0 \, \text{s}} = \frac{22.2222}{5.0} \, \text{m/s}^2 \approx 4.4444 \, \text{m/s}^2 \]

The problem asks for the answer to be expressed using two significant figures. Therefore, we round \(4.4444 \, \text{m/s}^2\) to two significant figures.

\[ a \approx 4.4 \, \text{m/s}^2 \]

Final Answer