Question

A driver of a truck travelling at 72 kmph, on turning a corner finds a child 42.5 m ahead. He applies brakes and decelerates the truck at the rate of 5ms-2, to just avoid the accident. The reaction time of the driver of the truck is​

Answer 1

Given:

A driver of a truck travelling at 72 kmph, on turning a corner finds a child 42.5 m ahead. He applies brakes and decelerates the truck at the rate of 5ms-2, to just avoid the accident.

To find:

Reaction time of accident?

Calculation:

• Initially velocity = 72 km/hr = 20 m/s.

Let reaction time of driver be t :

So, distance travelled before he braked:

$d = 20 \times t$

So, remaining distance between truck and child:

$x = 42.5 - 20t$

The driver then braked at 5 m/s².

$\implies \dfrac{ {v}^{2} - {u}^{2} }{2a} = 42.5 - 20t$

$\implies \dfrac{ {(0)}^{2} - {(20)}^{2} }{2( - 5)} = 42.5 - 20t$

$\implies \dfrac{ 400 }{10} = 42.5 - 20t$

$\implies 40 = 42.5 - 20t$

$\implies 20t = 2.5$

$\implies t = 0.125 \: sec$

So, reaction time of driver is 0.125 sec.