The table below shows how the braking distance x for a car depends on its initial speed u

u / ms-1 5.0 10 20 4
x / m 2.0 8.0 32 128
the reaction time of a driver is 0.60s. Calculate the sopping distance of the car when u= 30ms-1.

The mark scheme says:
Thinking distance= 30 X 0.6 =18m which I understand fully.
BRAKING DISTANCE =0.08 * U^2= 0.08 * 30^2= 72m IS THE BIT I DON’T UNDERSTAND. CAN SOMEONE PLEASE EXPALIN THE BRAKING DISTANCE STAGE AND WHY AND HOW YOU DO THIS BIT AS WELL AS ALL EQUATIONS INVOLVED!
Stopping distance= 18 +72= 90m which I understand fully.

please help.

Explain the working out of the braking distance for this question.

As physics - cylinder Thursday, November 9, 2017 at 7:37am
I wrote what I do know and the caps lock is what I dont know, and that is the working out for braking distance shown above is confusing to me.

As physics - Damon Thursday, November 9, 2017 at 8:39am
your table makes no sense to me

v = Vi + a t where t is AFTER 0.6 s
v = 30 + a t
so
x = Xi + Vi t + (1/2) a t^2

a will be negative of course
Xi is 18 when t = 0
x = 18 + 30 t + (1/2) a t^2

remember total stopping time = t + .6

As physics - cylinder Thursday, November 9, 2017 at 9:27am
I am in as and we dont use those symbols so im confused

Sorry for the repost i didnt understand and i just wanted to show how the working and answer went so someone can better help me

I had this question too and didnt understand it either when i went through thisquestionin a level we dont usae Xi or any of those please write in ful lsentencs ad clearly explain

I apologize for the confusion. Let me explain the concept of braking distance and how to calculate it in a simpler way.

Braking distance is the distance a car travels from the point when the brakes are applied until it comes to a complete stop. It is influenced by factors such as initial speed, reaction time of the driver, and the braking force applied.

In this case, the table provided shows the relationship between the initial speed (u) of the car and the braking distance (x) it takes to stop. To find the braking distance for a specific initial speed, such as u = 30 m/s, you can use the equation for braking distance:

Braking distance = (0.08 * u^2)

Let's substitute the value for u = 30 m/s into the equation:

Braking distance = (0.08 * 30^2)
= (0.08 * 900)
= 72 meters

So, when the initial speed of the car is 30 m/s, the braking distance is 72 meters.

To find the total stopping distance, you need to consider the thinking distance and the braking distance. The thinking distance is the distance the car travels during the driver's reaction time, which is given as 0.60 seconds in this question.

The thinking distance can be calculated by multiplying the initial speed by the reaction time:

Thinking distance = (u * reaction time)
= (30 * 0.60)
= 18 meters

The total stopping distance is then the sum of the thinking distance and the braking distance:

Total stopping distance = (thinking distance + braking distance)
= (18 + 72)
= 90 meters

Therefore, when the initial speed of the car is 30 m/s, the total stopping distance is 90 meters.