A car is being driven at 20 m / s when the driver sees a child run into the road. The driver’s usual reaction time is 0.70 s, but this is doubled because the driver is tired. Once the driver applies the brakes, the car is brought uniformly to rest in a further 3.3 s. What is the total distance travelled by the car between when the driver first sees the child to when the car stops?

Answer:

23) D

We know the initial velocity (u) = 20m/s

Final velocity (v) = 0 m/s (driver comes to a rest)

It is important to note that the driver applies the brake AFTER his reaction time is complete.
Reaction time = 0.7 x 2 (driver is tired) = 1.4s

So 1.4 s after the child is seen, the driver applies the brake.

We first need to find the distance travelled in the initial 1.4s
Distance = speed x time = 20 x 1.4 = 28m

To find the distance travelled in the latter 3.3s, we need to use a SUVAT equation.

The SUVAT equations are:

• s = ut + ½at²
• s = ½ (u + v)t
• v² = u² + 2as
• s = vt – ½at²

The best SUVAT equation to use is the second one. 

s = ½ (u + v)t
s = ½ (20 + 0) 3.3
s = ½ (20) 3.3
s = 10 x 3.3
s = 33m

Total distance covered = 33 + 28 = 61m