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25 July, 08:03

A Porsche challenges a Honda to a 400-m race. Because the Porsche's acceleration of 3.5 m/s² is larger than the Honda's 3.0 m/s², the Honda gets a 1.0 s head start. Who wins, and by how much time?

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  1. 25 July, 08:12
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    Answer: The Porsche Wins. Arrives 19secs earlier before the Honda.

    Explanation: The head start of 1secs corresponded with the difference in acceleration {3.5m/s² - 3m/s²}=0.5m/s²

    Using the first equation of motion we obtain the velocity which correspond to this acceleration (0.5m/s²) and time of 1secs where initial velocity u = 0

    V = u + at

    V = 0 + at

    V = 0.5 * 1 = 0.5m/s

    Now let find the velocity of each of the car.

    If V. a

    0.5m/s 0.5m/s²

    ... m/s. 3.5m/s²

    Velocity of porche Vp

    = (3.5/0.5) * 0.5 = 3.5 m/s

    Also if. V. a

    0.5m/s. 0.5m/s²

    ... m/s. 3 m/s²

    Velocity of Honda Vh

    = {3/0.5} * 0.5 = 3m/s

    So let's find the time t taken by both cars to cover the distance of 400m

    Recall,

    Velocity = distance/time

    Time t = distance/velocity

    For Porche, t = 400/3.5 = 114.29secs

    For Honda, t = 400/3 = 133.33secs

    Looking critically, we noticed that Porche car took shorter time.

    The difference In time is

    = (133.33 - 114.29) secs = 19.04secs
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