Mathematics

Problem

A particle moves along a straight line so that its velocity at time

t

seconds is given by

v(t)=5t\,e^{5t^{2}}

metres per second. a. (a) Find the displacement of the particle from

t=1\,\text{s}

t=3\,\text{s}

. b. (b) Suppose instead the velocity were

v(t)=k t\,e^{k t^{2}}

with

k>0

. Obtain a general expression for the displacement between

t=a

and

t=b

seconds in terms of

k

a

, and

b