The position of a particle moving in a straight line is described by x(t)=2t^ 3 -9t^…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
The position of a particle moving in a straight line is described by
x(t)=2t3−9t2+12t+5
where x is in metres and t in seconds.
(a) Obtain expressions for its instantaneous velocity and instantaneous acceleration.
(b) Calculate the numerical values of velocity and acceleration at t=2 s.
(c) Find the time(s) within 0 s≤t≤4 s when the particle is momentarily at rest.