For seconds, the position of a particle moving along the –axis is given by the…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
For 0≤t≤5 seconds, the position of a particle moving along the x–axis is given by the differentiable function
s(t)=t3−6t2+9t+4
where s(t) is measured in meters and t in seconds.
(a) Determine the particle’s velocity function v(t) and acceleration function a(t).
(b) Find all times in 0≤t≤5 when the particle changes direction. Justify your answer.
(c) Identify the time intervals on which the particle is speeding up and the intervals on which it is slowing down. Support your conclusions analytically.
(d) Describe the motion of the particle at t=1 and at t=4 in complete sentences that reference position, velocity, and acceleration.