Question

you are driving down a straight road at 54km/hr.when you are 30m from a side street a car abrutly pulls out in frount of you 1s to react tp the car and if your maximum acceleration is 5 m/s2 can you stop in time to aviod an accident?

Answer 1

You are driving down a straight road at 54km/hr. When you are 30m from a side street a car abruptly pulls out in front of you 1s to react to the car and if your maximum acceleration is 5 m/s2 can you stop in time to avoid an accident?

Solution:

Let:

$$v = 54 \text{ km/h} = 15 \text{ m/s}$$ $$S = 30 \text{ m}$$ $$a = 5 \text{ m/s}^2$$ $$t_0 = 1 \text{ s}$$

From: $S = \frac{1}{2} a t^2, v = a t$

The brake distance will be:

$$S = \frac{v^2}{2a} + v t_0$$ $$S = \frac{15^2}{2 \cdot 5} + 15 \cdot 1 = 37,5 \text{ m}$$

As the break distance is more than 30 m, you can not avoid an accident.