The velocity of a particle moving along the 𝑥-axis is given by 𝑓(𝑡)=9−3𝑡 cm/sec. Use a graph of 𝑓(𝑡) to find the exact change in position of the particle from time 𝑡=0 to 𝑡=4 seconds.

Answer 1

if 𝑓(𝑡)=9−3𝑡 , represents the velocity, then the displacement function would be
s(t) = 9t - 3/2 t^2 + c

s(0) = 0-0 + c
s(4) = 36 - 3/2(16) + c
= 36 - 24 + c = 12+c

change in position = 12+c - c = 12 cm