# A physics student drives a car with a total mass of 950 kg at a velocity of 25 m/s. She sees a speed zone ahead and slows down to a new velocity of 17 m/s in a time of 3.2 seconds. a) determine the original momentum of the car-and-student? b) what impulse was applied to the car? c) calculate the size and direction of the acting force.

(A) Momentum is given by the equation `p = mv` , so the initial momentum is `(950 kg)(25 m/s) = 23,750 kg*m/s` . Since we are given two significant figures, we should round to two significant figures for our answers, so the final answer is 2.4 *10^4 kg*m/s.

(B) The impulse is the change in momentum, so we need to find the final momentum, again by `p = mv` . The final momentum is `(950 kg)(17 m/s) = 16,150 kg*m/s` , which in two significant figures is 1.6 *10^4 kg*m/s.

(C) The direction of the force (applied by the friction of the brakes) is backwards, resisting the motion of the car. Its magnitude is the impulse divided by the time, `F = {Delta p}/{Delta t} = (16,150 kg*m/s)/(3.2 s) = 5046.875 N` , which in two significant figures is 5.0*10^3 N.

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