Question

A motorist sees the traffic light turns yellow when he is at 50 m from the intersection. If his speed at the moment of seeing traffic light is 90 mi/h, and His reaction time, before stepping on the brake is 0.50 s. What steady deceleration while braking will bring him to a stop right at the light? 1 mile/h = 0.45 m/s

Answer 1

The steady deceleration,
`a = -27.57 m/s^(2)`

Given:

1 mile = 0.45 m/s

initial distance of the motorist, s = 50 cm

speed of the motorist at the time he noticed the traffic light, v = 90 mi/h = 90
`* 0.45 = 40.5 m/s`

reaction time of motorist, t = 0.5 s

Solution:

Distance traveled before applying brakes, s' = v't

s' =
`40.5* 0.5 = 20.25 m/s`

The remaining distance traveled to the traffic light, s'' = 50 - s' = 50 - 20.25 = 29.75 m

Now, using third equation of motion to calculate steady deceleration:

`v^(2) - u^(2) = 2as`

where

v = final velocity

u = initial velocity

s = distance traveled

a = acceleration

Now,

`v^(2) - u^(2) = 2as`

In this eqn w.r.t the given case v = 0, as brakes are applied and the body will decelerate as a result of braking and u = v' and s = s'' = 29.75 m

Now, eqn becomes:

`0 - 40.5^(2) = -2a* 29.75`

`1640.25 = - 59.5a`

`a = -27.57 m/s^(2)`

where negative sign is indicative of deceleration