Question

1. 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? a - = 30 km/h + (2 m/s²)(3.6 s)

Explanation:

Step1: Convert initial speed to m/s

We know that \(1\ km = 1000\ m\) and \(1\ h=3600\ s\).
The initial speed \(v_0 = 30.0\ km/h=\frac{30\times1000}{3600}\ m/s=\frac{30000}{3600}\ m/s=\frac{25}{3}\ m/s\approx8.33\ m/s\)

Step2: Use the kinematic equation \(v = v_0+at\)

The acceleration \(a = 2.0\ m/s^{2}\) and time \(t = 3.6\ s\)
Substitute the values into the equation: \(v=\frac{25}{3}+2\times3.6\)
First, calculate \(2\times3.6 = 7.2\)
Then \(v=\frac{25}{3}+7.2=\frac{25 + 7.2\times3}{3}=\frac{25+21.6}{3}=\frac{46.6}{3}\approx15.5\ m/s\)
Convert back to \(km/h\): \(v = 15.5\times\frac{3600}{1000}=55.8\ km/h\)

Answer:

The car's final speed is approximately \(55.8\ km/h\)