Question

The reaction time for an automobile driver is 0.6 s. If the automobile can be decelerated at 5m/s^2 , calculate the total distance travelled in coming to stop from an initial velocity of 30 km/hr , after a signal is observed.

Answer 1

Approx. 12

Hope it helps. All the best.

Answer 2

Given:

Reaction time,t=0.6 s

Deceleration,a=-$5m/s^2$

Initial velocity,u=30 km/h=$30\times \frac{5}{18} m/s$

$1 km/hr=\frac{5}{18} m/s$

To find:

Total distance traveled in coming to stop from an initial velocity after a signal is observed.

Solution:

Final velocity,v=0

Distance traveled during reaction time=s=ut

$s=30\times \frac{5}{18}\times 0.6=5 m$

$v^2-u^2=2as$

$2as'=0-u^2=-u^2$

$s'=\frac{-u^2}{2a}$

Using the formula

$s'=-\frac{1}{2\times (-5)}(\frac{30\times 5}{18})^2$

$s'=6.94 m$

Total distance=s+s'=5+6.94=11.94 m