The driver of a car is going 90 km/hr suddenly sees a barrier40m ahead. It takes the driver .75 sec to apply the brakes, and the average acceleration during braking is -10m/s^2. Will the car hit the barrier and use calculation to show work.

90,000 m / 3600 s = initial speed = Ui

distance = .75 Ui + (Ui/2) t
to find t:
u = Ui - 10 t
when u = 0 we are stopped
so
t = Ui/10
so in the end

distance = .75 Ui + (1/2) Ui^2/10

Vo = 90,000m/3600s = 25 m/s.

d1 = Vo*t = 25m/s * 0.75s. = 18.75 m.
d2 = 40 - 18.75 = 21.25 m. = Required stopping distance.
Vf^2 = Vo^2 + 2a*d.
Vf = 0.
Vo = 25 m/s.
a = -10 m/s^2.

If d is => 21.25 m, the car will hit the barrier.

To determine whether the car will hit the barrier, we need to calculate the distance it will cover during the braking process. Here's how we can do that:

1. Convert the speed from km/hr to m/s by dividing it by 3.6.
90 km/hr ÷ 3.6 = 25 m/s

2. Use the formula: distance = initial velocity × time + 0.5 × acceleration × time squared.
Since the car is slowing down, the initial velocity is 25 m/s.
The time taken for braking is 0.75 seconds.
The average acceleration during braking is -10 m/s^2 (negative because the car is decelerating).
Plugging in the values, we have:
distance = 25 m/s × 0.75 s + 0.5 × -10 m/s^2 × (0.75 s)^2

3. Simplify and solve the equation.
distance = 18.75 m - 5.625 m = 13.125 m

The distance covered during braking is 13.125 meters. Since the barrier is 40 meters ahead, the car will hit the barrier.