Question

A driver is traveling 18.0 m/s when she sees a red light ahead. Her car is capable of decelerating at a rate of 3.65 m/s2. If it takes her 0.350 s to get the brakes on and she is 20.0 m from the intersection when she sees the light, will she be able to stop in time? How far from the beginning of the intersection will she be, and in what direction?

Answer 1

We use equation of motion,

$v^{2} = u^{2} +2 as$.

Here, v is final velocity of the body, u is initial velocity of the body, a is acceleration of the body and s is distance covered by body.

She travels a distance  = 18 x 0.350 = 6.3 m.

Therefore, she is [20 - 6.3] = 13.7 m from the intersection.

As her car is capable of decelerating at a rate of 3.65 m/s2

So,

$0 = (18 .0 m/s)^2 -2 \times (3.65 \ m/s^2) s \\\\ s = \frac{(18 m/s)^2 }{(2 \times3.65 m/s^2) } = 44 .38 \ m$.

She does not get stopped before the intersection.

Thus, she is 44.38-13.7 = 30.7 m ahead of the intersection.