Question

You're speeding at 82 km/h when you notice that you're only 13 m behind the car in front of you, which is moving at the legal speed limit of 60 km/h. You slam on your brakes, and your car negatively accelerates at 4.4 m/s2 .

What will be the distance between the cars at their closest approach?

Answer 1

Final speed of the car after applying the brakes = 60km/h where the closest approach occurs

60 km/h = 60 x 5/18 = 16.67 m/s

82 km/h = 82 x 5/18 = 22.78 m/s

V² = U² + 2aS

where V = final velocity = 16.67 m/s

U = iniitial velocity = 22.78 m/s

a = acceleration = -4.4 m/s2

S = (V²- U²)/2a = (16.67² - 22.78²)/-8.8 = 27.4 m

The distance covered by the other car in this time = 16.67 x time = 16.67 x (22.78-16.67)/4.4 = 23.15 m

Closest approach = 23.15 + 13 - 27.4 m = 8.75 m

Hence the closest approach is 8.75 meters