Dynamics

A car travels around a horizontal circular track of radius 45m.If the car increases its speed at a constant rate of 1.2m/s2 starting from rest, determine the time needed for it to reach an acceleration of 1.4m/s2. What is its speed at this instant?

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  1. Assuming 1.4m/s^2 is the combined radial acceleration (ar) and tangential (at).

    Note that the two accelerations are orthogonal (perpendicular) so that the combined acceleration can be found using Pythagoras theorem.

    ar=v²/r=v²/45
    at=1.2
    where v=tangential velocity

    When the combined acceleration = 1.4
    we have
    1.4²=1.2²+(v²/45)²
    v^4=(1.96-1.44)*45^2
    =1053
    => v=5.7 m/s

    At at=1.2 m/s from rest, it takes
    t=5.7/1.2=4.75 seconds

    check the numbers.

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