.A cart rolling down an incline for 5.0 seconds has an acceleration of 1.6 m/s2. If the cart has a beginning speed of 2.0 m/s, and its final

Question

.A cart rolling down an incline for 5.0 seconds has an acceleration of 1.6 m/s2. If the cart has a beginning speed of 2.0 m/s, and its final velocity of 10 m/s, what was the car’s displacement?

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Ben Gia 3 years 2021-07-29T19:32:29+00:00 1 Answers 39 views 0

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  1. Nho
    0
    2021-07-29T19:34:03+00:00
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    Use the formula,

    \Delta x=v_it+\dfrac12at^2

    where \Delta x is the cart’s displacement (from the origin), v_i is its initial speed, a is its acceleration, and t is time.

    \Delta x=\left(2.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(1.6\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2

    \implies\boxed{\Delta x=30\,\mathrm m}

    Alternatively, since acceleration is constant, we have

    \dfrac{v_f+v_i}2=\dfrac{\Delta x}t

    That is, we have these two equivalent expressions for average velocity, where v_f is the cart’s final velocity. Solve for \Delta x:

    \dfrac{10\frac{\rm m}{\rm s}+2.0\frac{\rm m}{\rm s}}2=\dfrac{\Delta x}{5.0\,\mathrm s}

    \implies\boxed{\Delta x=30\,\mathrm m}

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