What acceleration is needed to stop in time from hitting the wall?

Question

Chris drives a 1200 kg car straight at a brick wall. He is accelerating at a rate of 4 m/s^2. He started from rest and accelerated for 3 seconds, and began to hit the brakes when he was 9m away from the wall. 

 

What acceleration is needed to stop in time from hitting the wall?

Answer 1

He must bring his speed down to zero over a distance x = 9m.

 

v₂² - v₁² = 2ax

 

v₂ = 0 ⇒

 

a = -v₁²/(2x)

 

v₁ = a₀t = (4 m/s²)(3s) = 12 m/s

 

a = -(12 m/s)² / [2(9m)] = -8 m/s²

 

The minus sign means the acceleration is applied opposite to the direction of motion.