A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.2 m/s2. A green car arrives at

Question

A blue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.2 m/s2. A green car arrives at the position of the stop-light 7.5 s after the light had turned green. If t = 0 when the light turns green, at what time does the green car catch the blue car if the green car maintains the slowest constant speed necessary to catch up to the blue car?

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Sigridomena 2 weeks 2021-07-19T14:09:42+00:00 1 Answers 3 views 0

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    2021-07-19T14:11:12+00:00

    Answer:

    After 15 seconds, the green car will catch up with the blue car

    Explanation:

    Let the time for the green car to catch up with the blue car be T

    When the green car catches up to the blue car, the distances covered by each car after time T will be equal. Also, their velocities at that instant will be equal

    Distance covered by blue car after time T is given by: s = ut + 0.5 at²

    Where u = 0, a = 0.2 m/s², t = T

    S = 0.5 × 0.2 × T² = 0.1 T²

    Velocity of blue car, v = u+ at

    v = 0.2T

    Distance covered by green car at T is given as: S = Velocity × time

    Where v = 0.2T, t = T – 7.5 (since the blue car started 7.5 seconds earlier)

    S = 0.2T (T – 7.5)

    S = 0.2 T² – 1.5T

    Equating the distance covered by the two cars

    0.2T² – 1.5T = 0.1T²

    0.1T² – 1.5T = 0

    T(0.1T – 1.5) = 0

    T = 0 or

    T = 1.5/0.1 = 15 secs

    Therefore, after 15 seconds, the green car will catch up with the blue car

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