A car travels at a constant speed around a circular track whose radiu is 2.6 km. The goes once arond the track in 360s . What is the magnitu

Question

A car travels at a constant speed around a circular track whose radiu is 2.6 km. The goes once arond the track in 360s . What is the magnitude

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Eirian 5 years 2021-07-30T01:56:21+00:00 1 Answers 287 views 1

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  1. thienhuong
    1
    2021-07-30T01:57:38+00:00
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    Answer:

    Centripetal acceleration = 0.79 m/s²

    Explanation:

    Given the following data;

    Radius, r = 2.6 km

    Time = 360 seconds

    Conversion:

    2.6 km to meters = 2.6 * 1000 = 2600 meters

    To find the magnitude of centripetal acceleration;

    First of all, we would determine the circular speed of the car using the formula;

    Circular \; speed (V) = \frac {2 \pi r}{t}

    Where;

    • r represents the radius and t is the time.

    Substituting into the formula, we have;

    Circular \; speed (V) = \frac {2*3.142*2600}{360}

    Circular \; speed (V) = \frac {16338.4}{360}

    Circular speed, V = 45.38 m/s

    Next, we find the centripetal acceleration;

    Mathematically, centripetal acceleration is given by the formula;

    Centripetal \; acceleration = \frac {V^{2}}{r}

    Where;

    • V is the circular speed (velocity) of an object.
    • r is the radius of circular path.

    Substituting into the formula, we have;

    Centripetal \; acceleration = \frac {45.38^{2}}{2.6}

    Centripetal \; acceleration = \frac {2059.34}{2600}

    Centripetal acceleration = 0.79 m/s²

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