Question

Suppose a car is traveling at 19.3 m/s, and the driver sees a traffic light turn red. After 0.236 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 8.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light?

Answer 1

The total distance covered is
`D = 27.76 \ m`

Step-by-step explanation:

From the question we are told that

The initial speed of the car is
`u = 19.3 \ m/s`

The time taken before breaks where applied is
`t = 0.236 \ s`

The deceleration is
`a = 8.00 \ m/s^2`

The first distance covered before break was applied is mathematically evaluated as

`d = u * t`

substituting values

`d = 19.3 * 0.236`

`d = 4.484 \ m`

The distance covered after break has been applied is mathematically evaluated using the equation f motion as follows

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

The negative sign is because the car is decelerating and the final velocity is zero

`u^2 = 2as`

=>
`s = (u^2)/(2a)`

substituting values

`s = (19.3^2)/(2(8))`

`s = 23.28 \ m`

The total distance covered is

`D = d+s`

substituting values

`D = 4.484+ 23.28`

`D = 27.76 \ m`