Question

A car is running at a speed u. Seeing a child
on the road, the driver applies the brakes so
as to bring the car to a halt within a distance
S. Show that the reaction time of the driver
is 2 S/u.​

Answer 1

Explanation:

The car is running at speed u

let , the car applies brake with a decelaration of a

& the car will stop ( v = 0) after traversing the distance S & the time required ( response time ) will be t

we have to just find t ,

so applying formulae of kinematics,

v² = u² – 2 a s

or, a = u²/2s -------- eqn1 (v = 0)

then, apply,

v = u – at

or, t = u/a

now putting the value of a from eqn1, we get,

t = u * (2S/u²)

or, t = 2S/u.