Two objects and move along the same straight track with displacements and (in metres)

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Two objects

A

and

B

move along the same straight track with displacements

s_A(t)=4t^{2}+3t

and

s_B(t)=3t^{2}+7t

(in metres), where

t

is in seconds. (a) Write the expressions for their instantaneous velocities

v_A(t)

and

v_B(t)

. (b) Find the time when the two velocities are equal and state that common velocity (in m/s).