For , the velocity (in meters per second) of a particle moving along a horizontal…
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions
Problem
For t>0, the velocity v(t) (in meters per second) of a particle moving along a horizontal line satisfies the implicit equation
tv(t)+ln(v(t))=t2.
At t=1 second, the particle’s velocity is v(1)=1m/s.
(1) Part 1: Derive an explicit expression for the particle’s acceleration a(t) in terms of t and v(t).
(2) Part 2: Compute the acceleration at t=1 second.
(3) Part 3: Determine whether the speed of the particle is increasing or decreasing at t=1. Justify your answer numerically and analytically.