A particle moves along a straight line with velocity given by Time is measured in…
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)=t3−6t2+9t(meters per second),0≤t≤6.
Time t is measured in seconds and the origin is the particle’s starting position.
(a) Determine all times in the interval 0≤t≤6 at which the particle is at rest.
(b) For each sub-interval determined by those times, state the direction in which the particle is moving and justify your answer using the sign of v(t).
(c) Evaluate the displacement of the particle over the entire interval 0≤t≤6. Express your answer with correct units.
(d) Compute the total distance traveled by the particle on 0≤t≤6 and include units.