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

Answer:

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

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

       $u^2 = 2as$

=>    $s = \frac{u^2}{2a}$

substituting values

       $s = \frac{19.3^2}{2(8)}$

       $s = 23.28 \ m$

The total distance covered is  

    $D = d+s$

substituting values

     $D = 4.484+ 23.28$

     $D = 27.76 \ m$