The brochure advertising a sports car states that the car can be moving at 100.0 km/h, and stop in 37.19 meters. What is its average acceleration during a stop from that velocity? Express your answer in m/s2. Consider the car's initial velocity to be a positive quantity.
We know that
V = at ==> t = V/a,
where V is velocity, a is acceleration and t is the time of acceleration. Also we know that
L = at²/2 ==> a = 2L/t²,
where L is the stop distance. So,
a = 2L/t² = 2L/(V/a)² = 2L/(V²/a²) = 2a²L/V²