A particle moves along a straight line so that its velocity
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A particle moves along a straight line so that its velocity, in metres per second, is given by
v(t)=t2−5t+6,0≤t≤6,
where t is measured in seconds.
(a) Determine all values of t in [0,6] at which the particle is at rest.
(b) On which sub-intervals of [0,6] is the particle moving in the positive direction and on which sub-intervals is it moving in the negative direction? Show your reasoning clearly.
(c) Compute the total distance travelled by the particle on [0,6] and compare it to its net displacement over the same interval. Include units in your answer.