Deceleration and length

Question

Assuming that the maximum deceleration of a car when full braking is applied is 0.8g, find the length of run required to pull up from

a) 50 km/h

b) 100km/h

Answer 1

First lets convert everything into the same units:

a = -0.8g = -0.8*9.8m/s² = -7.84 m/s²

(50 km/h)(1000 m/km)(1 h/3600 s) = 13.889 m/s

(100 km/h)(1000 m/km)(1 h/3600 s) = 27.778 m/s

 

Distance, initial and final velocities, and acceleration are related by the equation

v_f² = v_i² + 2aΔx

 

In both cases, your final velocity is 0. You can plug in the values you have in each part and solve for the distance, Δx.