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