you are driving at 18m/s down Lyndale avenue. A car backs out a driveway 25 meters in front of you. You continue at that speed while your brain processes the danger which takes 0.25 seconds. You then slam on the brakes and your car has an acceleration of -5.4m/s^2. Do you stop before reaching the driveway(and hitting the car)? Show your work. This is a two-part problem with constant speed and braking.

Hello!

For this, first let's calculate time of stop:

t = (V - Vi) / a

Replacing:

t = (0 m/s - 18 m/s) / -5,4 m/s^2

Resolving:

t = -18 m/s / -5,4 m/s^2

t = 3,33 s + 0,25 s = 3,58 s

Now lets calculate distance traveled, with formula:

d = Vi*t + (a*t^2)/2

Replacing:

d = 18 m/s * 3,58 s + (-5,4 m/s^2 * (3,58 s)^2) /2

Resolving:

d = 64,44 m + (-34,604 m)

d = 29,83 m

Then, the vehicle will CRASH

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