hs

Question $3.$ The acceleration of a robot as it moves along a straight line in the

horizontal xaxis is given by

a $=$ e

kt$(2$ cos $!$t $+3$ sin $!$t$)$; k $6=0$; $!6=0$; $(2)$

where k and $!$ are positive constants and the time t is in seconds. If the initial position

x$0=1$ m and initial velocity v$0=2$ m$=$ sec when t $=0$;

$($i$)$ determine the velocity v $=$ v$($t$)$ as a function of time

$($ii$)$ determine the position x $=$ x$($t$)$ as a function of time

$($iii$)$ choose suitable values for k$,!$ and time interval $0$ t to plot the x t; v t

and a