A particle moves along a straight line with velocity given by

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A particle moves along a straight line with velocity given by v(t)=5sin⁡(2t)+3t  (SI units)v(t)=5\sin(2t)+3t\;(\text{SI units}). Consider the time interval 0≤t≤π s0\le t\le \pi\,\text{s}. (i) Derive an expression for the instantaneous acceleration of the particle. (ii) Determine the maximum and minimum values of the acceleration in the given interval. (iii) Find all instants within 0≤t≤π0\le t\le \pi when the particle momentarily comes to rest. Evaluate the acceleration at each of these instants.

Related theory

Browse the problem library