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7 May, 08:38

The velocity of an object is given by the expression v (t) = 3.00 m/s + (4.00 m/s^3) t^2, where t is in seconds. Determine the position of the object as a function of time if it is located at x = 1.00 m at time t = 0.000 s

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  1. 7 May, 11:51
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    Position of object is;

    s (t) = 4t³/3 + 3t + 1

    Explanation:

    We are told that the velocity has an expression;

    v (t) = 3.00 m/s + (4.00 m/s³) t²

    Now, to get the expression for the position (s (t)) of the object, we have to integrate the velocity expression. Thus;

    s (t) = ∫3 + 4t²

    s (t) = 3t + 4t³/3 + c

    Now, we were told that at x = 1.00 m, time t = 0.000 s

    Thus, plugging the values in;

    1 = 3 (0) + 4 (0³/3) + c

    c = 1

    Thus, the expression for the position of the object is;

    s (t) = 4t³/3 + 3t + 1
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