A cyclist rides down a long straight road at a velocity (in m/min) given by v(t)equals400minus20t, 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?

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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