# Physics

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A car traveling at a constant speed of 33 m/s passes a trooper hidden behind a billboard. One second later the trooper starts the car with a constant acceleration of 2.62 m/s^2.
How long after the trooper starts the chase does he overtake the speeding car? (answer in units of s)

• Physics -

d1 = Vo*(t+1) + 0.5at^2,
d1 = 33(t+1) + 0.5*0*(t+1)^2,
d1 = 33(t+1) + 0 = 33t + 33.

d2 = 0 + 0.5*2.62*t^2,
d2 = 1.31t^2.

d1 = d2,
33t + 33 = 1.31t^2,
1.31t^2 - 33t - 33 = 0,
Solve using Quadratic Formula and get:
t = 26.15s, and -0.96s.
Use the positive valuie:
t = 26.15s.

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