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A car accelerates in the +x direction from rest with a constant acceleration of a1 = 1.76 m/s2 for t1 = 20 s. At that point the driver notices a tree limb that has fallen on the road and brakes hard for t2 = 5 s with a constant acceleration of a2 = -5.93 m/s2.

Write an expression for the car's speed just before the driver begins braking, v1.

If the limb is on the road at a distance of 550 meters from where the car began its initial acceleration, will the car hit the limb?

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  1. V1 = a1*t1 = 1.76 * 20 = 35.2 m/s.
    d1 = 0.5a1*t1^2 = 0.88*20^2 =

    V2 = V1 + a*t = 35.2 - 5.93*5 = 5.55 m/s. The 5-second deceleration is not enough to bring the car to a full stop.

    d2 = V1*t + 0.5a*t^2.
    d2 = 35.2*5 - 0.5*5.93*5^2 =

    d = d1+d2 =

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