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.

Question

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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Savannah 2 weeks 2021-09-14T22:50:21+00:00 1 Answer 0

Answers ( )

    0
    2021-09-14T22:51:39+00:00

    Answer:

    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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