# Physics question from Ari's problem set

Hello, I feel like there is not sufficient data given to solve this one. I couldn’t get to the answer without displacement. Can somebody explain? Thank you!

The equations we’ll use are:

1. v=u+at where v is final velocity, u is initial velocity, a is acceleration, and t is time.
2. s=ut+1/2.a.t^2 where s is displacement.

Given:

Initial velocity of the police officer (u) = 0 m/s (since the officer starts from rest) Acceleration (a) = 5.5 m/s²
Velocity of the motorist (v) = 24.75 m/s

Finding the time taken for the officer to catch the motorist:

Using the first equation:

v=u+at
24.75=0+5.5t
t≈4.5 seconds

So, it takes approximately 4.5 seconds for the police officer to catch up with the motorist.

Finding the displacement of the officer as he overtakes the motorist:

Using the second equation:

s=ut+1/2.at^2
s=0. 4.5+1/2. 5.5. (4.5)^2
s≈55.6875 meters

So, the displacement of the officer as he overtakes the motorist is approximately 55.69 meters.

Hey, thanks for your reply, it seems like a great explanation, but the answers actually say 9 seconds; and 222.75 meters. Your explanation seems correct, but the answers differ for some reason

Perfect, thank you so much!

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