Question

Frank, driving at 30.0 m/s, enters a one-lane tunnel. He then observes a slow-moving van 150.0 meters ahead traveling with speed 1.0 m/s (because it has engine trouble). He applies the brakes immediately to decelerate at a constant rate but still hits the van. From the damage, it is determined that he was traveling at 5.0 m/s when the collision occurred. Determine the magnitude of Frank's deceleration as he applied the brakes.

Answer 1

Relative speed of the Frank's van u​​​​=30-1= 29 m/s

Distance travel during deceleration d=150 m

The speed of the ven when collision occurred v=5 m/s

Since Deceleration is a constant rate means deceleration is constant. So

Using equation of the motion

v^2=u^2-2ad

a=u^2-v^2 /2d

a=29^2-5^2/(2×150)

a=(841-25)/(300)

a=2.72 m/s^2. Answer