The driver of a car going 90.0 km/h suddenly sees the lights of a barrier 35.0 m ahead. It takes the driver 0.75 s to apply the brakes, and the average acceleration during braking is -10.0 m/s2.

(b) What is the maximum speed at which the car could be moving and not hit the barrier 35.0 m ahead? Assume that the acceleration doesn't change.

I needed help with that one..

the steps on how to achieve the answer would be helpful k thx

To determine the maximum speed at which the car could be moving and not hit the barrier, we need to find the distance it will take for the car to come to a stop.

First, let's find the time it takes for the car to come to a stop using the average acceleration:

Given:
Initial velocity, u = 90.0 km/h
Acceleration, a = -10.0 m/s^2
Time, t = 0.75 s

We need to convert the initial velocity from km/h to m/s:

u = 90.0 km/h * (1000 m/1 km) * (1 h/3600 s)
u = 25.0 m/s

Now, we can use the kinematic equation:

v = u + at

Where:
v = final velocity (which is 0 m/s since the car comes to a stop)
u = initial velocity
a = acceleration
t = time

Substituting the given values:

0 = 25.0 m/s + (-10.0 m/s^2) * t

Solving for t:

-25.0 m/s = -10.0 m/s^2 * t
t = (-25.0 m/s) / (-10.0 m/s^2)
t = 2.5 s

Now, we can calculate the distance covered during this time:

s = ut + (1/2)at^2

Substituting the known values:

s = (25.0 m/s) * (2.5 s) + (1/2) * (-10.0 m/s^2) * (2.5 s)^2
s = 62.5 m - 31.25 m
s = 31.25 m

Thus, the car would need a distance of 31.25 m to come to a stop.

To not hit the barrier positioned 35.0 m ahead, the car's speed must be lower than the maximum speed that allows it to stop before reaching the barrier.

Therefore, the maximum speed at which the car could be moving and not hit the barrier is 31.25 m/s.

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