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## Homework Statement

The speed limit in a school zone is 40 km/h (about 25 mi/h). A driver sees a child run onto the road 13 m ahead of his car. He applies the breaks, and the car decelerates at a uniform rate of 8.0 m/s^2. If the driver's reaction time is 0.25 s, will the car stop before hitting the child?

## Homework Equations

d = Vot + 1/2at^2

V^2 = Vo^2 + 2ad

## The Attempt at a Solution

40 km/h x [1000 m/1 km] x [1 h/3600 s] = 11 m/s

Vo = 11 m/s

X = ?

Xo = 0

a = -8.0 m/s^2

t = 0.25 s

X - Xo = Vot + 1/2at^2

X = (11 m/s)(0.25 s) + 1/2(-8.0 m/s^2)(0.25 s)^2

= 2.5 m

Vo = 11 m/s

V = 0

X = ?

Xo = 2.5 m

a = -8.0 m/s^2

V^2 = Vo^2 + 2a(X - Xo)

X = Xo + [V^2 - Vo^2/2a]

= 2.5 + [0 - (11 m/s)^2/2(-8.0 m/s^2)

= 10 m

Therefore, 2.5 m + 10 m = 12.5 m, and the car will stop in time.

Seems right, can anybody please verify this outcome?