Question

a driver can stop his car from red signal at a distance of 20m when he is driving at 36kmph,41.25m when driving at 54kmph.find reaction time

Answer 1

Given info : a driver can stop his car from red signal at a distance 20 m when he is driving at 36 km/h and 41.25 m when driving at 54 km/h.

To find : time of reaction of car.

Solution : let t is time of reaction.

Using formula, s = ut + u²/2a

case 1 : s = 20m , u = 36 km/h = 36 × 5/18 = 10 m/s

so, 20 = 10t + (10)²/2a

⇒2 = t + 5/a ......(1)

Case 2 : s = 41.25 m, u = 54 km/h = 54 × 5/18 = 15 m/s

so, 41.25 = 15t + (15)²/2a

⇒ 41.25 = 15t + 225/2a

⇒2.75 = t + 7.5/a ......(2)

From equation (1) and (2) we get,

2.75 - 2 = 7.5/a - 5/a

⇒0.75 = 2.5/a

⇒a = 2.5/0.75 = 10/3 m/s²

From equation (1)

2 = t + 5/(10/3)

⇒2 = t + 3/2

⇒t = 0.5 sec

Therefore the time of reaction is 0.5 sec