Two cars, and , start from the same point on a straight road at the same instant.…
MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Two cars, A and B, start from the same point on a straight road at the same instant. Their respective positions (in metres from the starting point) after t seconds are given by
sA(t)=2t2+5t+10,sB(t)=3t2+t+4.
(i) Obtain the instantaneous velocity functions vA(t) and vB(t) for the two cars.
(ii) Find the time at which both cars are moving with the same velocity.
(iii) At the time calculated in part (ii), determine which car is ahead and by how many metres.