geometry

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a car traveling at 30 meters per second begins to slow down at a constant rate. after 2 seconds its velocity is 16 meters per second. write an equation that represents the cars velocity v after t seconds

  • geometry -

    Let the acceleration (really deceleration) be a
    so v = at + c
    when t=0 , v = 30
    30 = 0 + c, --> c=30
    so v = at + 30
    when t=2, v = 16
    16 = 2a + 30
    2a = -14
    a = -7

    v = -7t + 30

  • geometry -

    I just solved your question using Calculus, but I am not sure if you know Calculus, so ....

    Treat your data two ordered pairs (0,30) and (2,16)
    where the first coordinate is time and the second is velocity
    slope = (30-16)/(0-2) = -7
    so v = -7t + b , using the old y = mx + b format
    but (0,30) must satisfy this
    30 = 0 + b
    b = 30

    so v = -7t + 30 , as before

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