A truck on a straight road starts from rest, accelerating at 2.00m/s^2 until it reaches a speed of 20.0m/s. Then the truck travels for 20.0s

Question

A truck on a straight road starts from rest, accelerating at 2.00m/s^2 until it reaches a speed of 20.0m/s. Then the truck travels for 20.0s at constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00s.
(a) How long is the truck in motion?
(b) What is the average velocity of the truck for the motion described?

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Cherry 5 years 2021-07-27T11:06:39+00:00 1 Answers 30 views 0

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  1. Nem
    0
    2021-07-27T11:07:49+00:00
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    Answer:

    Explanation:

    a )

    Time to reach the speed of 20 m/s with an acceleration of 2 m/s² can be calculated as follows .

    v = u + a t

    20 = 0 + 2 t

    t = 20 /2 = 10 s .

    Total time = 10 s + 20 s + 5 s = 35 s .

    b) Average velocity = Total distance travelled / total time

    Distance travelled in first 10 s

    S₁ = ut + 1/2 a t²

    = 0 + .5 x 2 x 10²

    = 100 m

    Distance travelled in next 20 s

    S₂= 20s x 20 m/s  = 400 m

    Distance travelled in last 5 s .

    deceleration in last 5 s

    v = u + at

    0 = 20 m/s + a x 5

    a = – 4 m/s²

    v² = u² – 2 a s

    0 = (20 m/s)² – 2 x 4 m/s² x s

    s = 50 m

    S₃ = 50 m

    Total distance = S₁ + S₂ + S₃

    = 100 m + 400 m + 50 m

    = 550 m .

    Average velocity = 550 m / 35 s

    = 15.71 m /s .

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