Verified answer

so we know that the initial speed v0= 40 km/h = 40/3.6 m/s = 11.11 m/s

the acceleration a = - 8.0 m/s²

the distance x = 13 m

First we must know how far he will be before he starts braking (so after 0.25s):

x = v * t

x = 11.11 * 0.25

x = 2.775 m

The driver will have traveled 2.775 m before he uses his brakes.

So we know that our starting distance is 2.775 m

x0 = 2.775m

Now we need to know when he will have stopped.

x = x0 + v0 * t + a * t² / 2

We do not yet know t, so let's calculate that first:

11.11 m/s - t * 8 m/s² = 0

Since each second he will lose 8 m/s of his velocity.

8t = 11.11

t = 11.11 / 8

t = 1.38875 s

So the car stops after 1.39 s of braking

Now we can fill everything in:

x = x0 + v0 * t + a * t² / 2

x = 2.775 + 11.11 * 1.38875 - 8 * 1.38875² / 2

x = 7.714 m

So the car will stand still after 7.714 m after he saw the kid (including his reaction time).

Luckily, the poor child will be saved from a horrible death.

No, vacationing down a slope would not unavoidably recommend you're accelerating. If the up-slope forces (by way of friction) tournament the down-slope forces (by way of gravity), then your internet rigidity would be 0, so your acceleration would be 0. faster or later, she could have started moving, and might have sped up from 0 to her contemporary velocity. however the project isn't fascinated by that part of her holiday. it could take place in actual existence, under the staggering circumstances. it may count on the slope perspective, the coefficient of kinetic friction, and the rigidity by way of air resistance all having merely the staggering values.