Suppose that a particle moves along a straight line with velocity v ( t ) = 12 − 3 t , where 0 ≤ t ≤ 1.5 (in meters per second).

Question

Find the formula for the displacement of the particle and the total distance it has traveled at time  seconds.

Displacement at time 

Total distance traveled is    meters in 1.5 seconds

Answer 1

v(t) = 12-3t

s(t) = integral or antiderivative of v(t)

s(t) = 12t -(3/2)t^2 + c where c= initial starting point, which seems to be zero

s(1.5) = 12(1.5) - (3/2)(3/2)^2 = 18 - 27/8 = 18-3.375 = 14.625 meters

or if c= some non-zero number it cancels out when you subtract s(0)

s(1.5)-s(0) = 14 5/8 - 0 = 14 5/8 = 14.625 meters = displacement = distance traveled