Question
A car moves along a straight road in such a way that its velocity (in feet per second) at any time t (in seconds) is given by v(x) = 3x sqrt(9-x^2) on an interval of 0,3.
Find the distance traveled by the car in 3 seconds.
Find the distance traveled by the car in 3 seconds.
Answers
Reiny
v(x) = 3x sqrt(9-x^2) = 3x(9-x^2)^(1/2)
s(x) = -(9-x^2)^(3/2) + c
s(0) = -27 + c
s(3) = 0 + c
distance = (0 + c) - (-27 + c) = 27 ft
s(x) = -(9-x^2)^(3/2) + c
s(0) = -27 + c
s(3) = 0 + c
distance = (0 + c) - (-27 + c) = 27 ft