Use the formulas and rules of differentiation to find the de

Use the formulas and rules of differentiation to find the derivative of each function A particle moves along a straight line with equation of motion s(t) = t3 - 9t2 + 24t for t 0. where t is measured in seconds and s in feet. Find the velocity and acceleration of the particle at time t. When is the particle at rest? What is its acceleration then? When is the particle moving in the positive direction? in the negative direction? Find the total distance traveled during the first 6 seconds.

Solution

s(t)=t³-9t²+24t

vel=s\'(t)=3t²-18t+24

acc=6t-18

particle at rest at v=0

3t²-18t+24=0

t²-6t+8=0

t=2,4

particle is moving in +ve direection when v is +ve

in -ve dir when v is -ve

dis travelled in 6sec=216-324+144=36