Mathematics

Problem

A particle moves along a line with velocity given by

v(t)=3t^{2}-12t+5

, where

t

is measured in seconds and

v

in meters per second. (a) Determine the particle’s acceleration function

a(t)

and state the units. (b) Evaluate

a(1)

and

a(3)

. Include units with each answer and interpret what the signs of these values indicate about the motion. (c) Find all values of

t

for which the particle transitions between speeding up and slowing down. Justify your conclusion.