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28 November, 16:58

A commuter backs her car out of her garage with an acceleration of 1.40 m/s^2. (a) How long does it take her to reach a speed of 2.00 m/s? (b) If she then brakes to a stop in 0.800 s, what is her deceleration?

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  1. 28 November, 18:04
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    a) It takes her 1.43 s to reach a speed of 2.00 m/s.

    b) Her deceleration is - 2.50 m/s²

    Explanation:

    The equation of velocity for an object that moves in a straight line with constant acceleration is as follows:

    v = v0 + a · t

    Where:

    v = velocty.

    v0 = initial velocity.

    a = acceleration.

    t = time.

    a) Using the equation of velocity, let's consider that the car moves in the positive direction. Then:

    v = v0 + a · t

    2.00 m/s = 0 m/s + 1.40 m/s² · t

    t = 2.00 m/s / 1.40 m/s²

    t = 1.43 s

    It takes her 1.43 s to reach a speed of 2.00 m/s

    b) Let's use again the equation of velocity, knowing that at t = 0.800 s the velocity is 0 m/s:

    v = v0 + a · t

    0 = 2.00 m/s + a · 0.800 s

    -2.00 m/s / 0.800 s = a

    a = - 2.50 m/s²

    Her deceleration is - 2.50 m/s²
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