The velocity of a particle moving along a line is a function of time given by v ( t )

Question

The velocity of a particle moving along a line is a function of time given by  . Find the distance that the particle has traveled after  seconds if it started at  seconds.

Answer 1

v = 72/T^2 + 8t + 7

d = the integral of v = -72/t + 4t^2 + 7t + c where c is an unknown constant

f(8) = -72/8 + 4(8^2) + 7(8) + c = -9 + 256 + 56 + c = 303+c

f(0) = c

f(8) - f(0) = 303 + c - c = 303

distance traveled in 8 seconds is 303