Question

Stan is speeding in a silver sedan at 77 m/s when he suddenly sees a stopped police car 90 m in front of him. He immediately applies the brakes and slows to 38 m/s by the time he is next to the police car. Find: (a) the acceleration, (b) how much time elapses?

Answer 1

The acceleration of Stan is 24.92 m/s².

The elapsed time during Stan's motion is 1.57 s.

What is acceleration?

Acceleration is the rate of change of velocity with time. Acceleration is vector quantity because it has magnitude and direction. It increases with increase in speed of an object.

The acceleration of Stan is calculated as follows;

$v^2 = u^2 + 2as\\\\ a = \frac{v^2 - u^2}{2s} \\\\ a = \frac{(38)^2 - (77)^2}{2(90)} \\\\ a = -24.92 \ m/s^2\\\\ |a| = 24.92 \ m/s^2$

The time of motion of Stan is calculated by using the first kinematic equation of motion as shown bellow;

$a = \frac{v- u}{t} \\\\ t = \frac{v- u}{a} \\\\ t = \frac{38-77}{-24.92} \\\\ t = 1.57 \ s$

Thus, the acceleration of Stan is 24.92 m/s² and the elapsed time during Stan's motion is 1.57 s.

Learn more about acceleration here: https://brainly.com/question/605631