First slide

The 3 equation for uniform acc

Question

A vechicle moving with a speed of 36 km/h sees a red light ahead dg applies brakes and stops after covering 10 m distances. If moving at a speed of 72 km/h then applying brakes it stops after covering 30 m distance. Assuming same reaction time and same deceleration in each case, the distance covered when brakes are applied on the vehicle when it is moving at 54 km/h is

Moderate

A

20 m
B

40 m
C

18.75m
D

9.37m

Solution

Let, the time in which the vehicle keeps on moving with the same speed before brakes are actually applied, i.e., reaction time be t₀. Then
In first case u² = 2a (x - x₀)
or ${(\frac{36 Ã 5}{18})}^{2} = 2 a (10 â 10 t_{0}) . . . (1)$
In second case,
${(\frac{72 Ã 5}{18})}^{2} = 2 a (30 â 20 t_{0}) . . . . (2)$
Similarly, ${(\frac{54 Ã 5}{18})}^{2} = 2 a (s â 15 t_{0}) . . . . (3)$
Dividing (1) by (2),t_o = (1/ 2) sec
Dividing eq. (t) by eq. (g) and putting
t₀ =1/2, we get
s =18.75m

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