A particle moves along a straight line with velocity given by meters per second
MATHEMATICS · Multi-part · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
A particle moves along a straight line with velocity given by v(t)=3t2+2 meters per second, where t is measured in seconds.
The particle starts at time t=0 and travels until time t=T.
Parts:
(a) Write, but do not yet evaluate, a definite integral that represents the average velocity of the particle over the time interval [0,T]. Use the definition of average value.
(b) Evaluate the integral from part (a) and obtain an explicit algebraic expression for the average velocity in terms of T.
(c) Given that the average velocity over [0,T] is required to be exactly 10 m/s, solve for the value of T. Show all algebraic steps clearly.
(d) Interpret the meaning of your result from part (c) in the context of the particle’s motion. Include appropriate units in your explanation.