Share
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
Question
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?
in progress
0
Physics
3 years
2021-08-24T21:48:59+00:00
2021-08-24T21:48:59+00:00 1 Answers
38 views
0
Answers ( )
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