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22 January, 18:33

A cyclist rides down a long straight road at a velocity (in m/min) given by v (t) = 400-20t, for 0≤t≤10, where t is measured in minutes.

A. How far does the cyclist travel in the first 5 min?

B. How far does the cyclist travel in the first 10 min?

C. How far has the cyclist traveled when her velocity is 250 m/min?

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  1. 22 January, 18:43
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    A. 1,500m

    B. 2000m

    C. 1875m

    Step-by-step explanation:

    A. Here, we simply substitute the value of t in the equation.

    t = 5min

    V (t) = 400 - 20t

    = 400 - 20 (5)

    = 400 - 100 = 300m/min

    Now we know that distance = speed * time = 300 * 5 = 1,500m

    2. Substitute t = 10

    V = 400 - 20 (10) = 400 - 200 = 200m/min

    Distance = speed * time = 200 * 10 = 2000m

    3. Here we need to calculate time

    Rearranging the equation:

    20t = 400 - V (t)

    20t = 400 - 250

    20t = 150

    t = 150/20 = 7.5min

    Distance traveled = 250 * 7.5 = 1875m
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