Question

a car is moving at 30.0 km/h when it accelerates at 2.0 m/s² for 3.6 s. what is the cars final speed?
$v_{f}=30km/h+(2m/s^{2})(3.6s)$

Explanation:

Step1: Convert units

Convert \(v_{i} = 30.0\ km/h\) to \(m/s\).
\(v_{i}=30\times\frac{1000}{3600}\ m/s=\frac{30000}{3600}\ m/s=\frac{25}{3}\ m/s\approx8.33\ m/s\)
\(a = 2.0\ m/s^{2}\), \(t = 3.6\ s\)

Step2: Use the kinematic formula

The kinematic formula \(v_{f}=v_{i}+at\)
Substitute the values:
\(v_{f}=\frac{25}{3}+2\times3.6\)
\(v_{f}=\frac{25}{3}+7.2\)
\(v_{f}=\frac{25 + 21.6}{3}\)
\(v_{f}=\frac{46.6}{3}\approx15.53\ m/s\)
Convert \(v_{f}\) to \(km/h\)
\(v_{f}=15.53\times\frac{3600}{1000}\ km/h\)
\(v_{f}=15.53\times3.6\ km/h = 55.908\ km/h\approx56\ km/h\)

Answer:

\(56\ km/h\)