how to work out braking distance of a car

Question

I'm stuck on a question where I have been given a speed lets say (x)MPH and a reaction time (Y)seconds and a rate of constant deceleration at a rate of (z)m/s^2 I'm not sure how I go about working this put tho

I have to draw a velocity against time graph for this

Answer 1

If you want to find the distance d required to come to a stop starting at some initial speed v, with braking acceleration a, use the kinematic relation 

 

v_f² - v_i² = 2ad

 

v_i = initial speed at the moment braking begins = v

v_f = final speed = 0 (comes to a full stop)

 

-v² = 2ad

 

d = -v²/(2a)

 

If you want d in meters, convert v to m/s, plug in a in m/s² with a negative sign (i.e. a deceleration, since braking opposes the direction of motion).  

 

I will make up a simple example, which should make this more clear.  (The numbers may not be realistic, but the important thing is to see the method!):

 

Suppose a vehicle is traveling at a constant speed of 20 m/s.  The driver sees a hazard ahead, and decides to apply the brakes.  There is a 5 second delay (i.e. reaction time) between seeing the hazard and applying the brakes.  During those 5 seconds, the car travels a distance 

 

d₁ = (20 m/s)(5s) = 100 m

 

At the end of d₁, the brakes are applied.  Suppose the brakes decelerate the vehicle at a constant rate of 4 m/s².  The acceleration is

 

a = -4 m/s²

 

The vehicle comes to a stop over an additional distance of

 

d₂ = -v²/(2a) = -(20 m/s)² / [2(-4 m/s²)] = 50 m

 

TOTAL distance traveled from moment the hazard is detected until coming to a full stop is

 

d = (travel distance due to delayed reaction) + (braking distance) = d₁ + d₂

 

d = d₁ + d₂ = (100 + 50) m = 150 m

 

This should help.