A cyclist rides down a long straight road at a velocity​ (in m/min) given by ​v(t)equals400minus20​t, for 0less than or equalstless than or

Question

A cyclist rides down a long straight road at a velocity​ (in m/min) given by ​v(t)equals400minus20​t, for 0less than or equalstless than or equals10. a. How far does the cyclist travel in the first 6 ​min? b. How far does the cyclist travel in the first 10 ​min? c. How far has the cyclist traveled when his velocity is 290 ​m/min?

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Ngọc Hoa 3 years 2021-08-24T21:48:59+00:00 1 Answers 34 views 0

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    2021-08-24T21:50:03+00:00

    Answer:

    a. 2040 m

    b. 3000 m

    c. 1697.5 m

    Explanation:

    Given that:

    v(t) = 400 – 20t

    0 ≤ t ≤ 10

    We can get the formula for distance traveled by integrating the velocity, v(t), with respect to time:

    => s(t) = 400t – 10t²

    a. First 6 mins:

    t = 6 mins

    s(t) = 400(6) – 10(6)²

    s(t) = 2400 – 360

    s(t) = 2040m

    b. First 10 mins:

    t = 10 mins

    s(t) = 400(10) – 10(10)²

    s(t) = 4000 – 1000

    s(t) = 3000 m

    c. When v(t) =290 m/mins

    We insert this into the v(t) equation so we can find time t.

    v(t) = 400 – 20t

    290 = 400 – 20(t)

    20t = 400 – 290

    20t = 110

    t = 110/20 = 5.5 mins

    Now we insert that into the s(t) equation:

    s(t) = 400(5.5) – 10(5.5)²

    s(t) = 2200 – 302.5

    s(t) = 1697.5 m

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