Billy Sue is speeding down a country road in his new monster truck at a constant 32 m/s when he goes over a hill and spots a cow standing in the middle of the road. The cow is 45m in front of him. If he reacts immediately upon viewing the cow, and his braking acceleration is 20 m/s 2 , can he stop in time to avoid hitting the cow?

He won't stop on time, the distance his car traveled during the braking is greater than 45 m.

Explanation:

Given;

initial velocity of Billy's car, u = 32 m/s

his braking acceleration, -a = 20 m/s

his final velocity when the car stops, v = 0

Apply the following kinematic equation to determine the distance traveled by Billy's car during the braking acceleration;

v² = u² + 2as

0 = 32² + (2 x -9.8)s

0 = 32² - 19.6s

19.6s = 32²

s = (32²) / (19.6)

s = 52.25 m

The distance traveled is greater than 45 m, thus Billy's car will hit the cow.

when the velocity of a mass on a spring is zero, the acceleration is at a maximum .