A body is moving in a straight line along x-axis

motioninstraightline
cbse

#1

A body is moving in a straight line along x-axis. Its distance from the origin is given by the equation x=${{at}^{2}}$ - ${{bt}^{3}}$, where x is in metre and t is in second. Find
(i) the average speed of the body in the interval t = 0 and t = 2 s and
(ii) its instantaneous speed at t = 2s


#2

The given equation x = ${{at}^{2}}$ —${{bt}^{3}}$
(i)If t = 0 ${ x }{ 0 }$
If t= 2s ${ x }
{ 2 }$ = 4a - 8b
∆x = ${ x }{ 2 }$ -
${ x }
{ 0 }$ = 4a-8b = 0
4a-8b
∆t = 2-0 = 2
Average speed in the given interval of time
${ v }_{ av }$ = ∆x / ∆t = 4a-8b / 2 = 2a-4b
(ii)Instantaneous speed
v =dx/dt = d/dt (${{at}^{2}}$ - ${{bt}^{3}}$)
= 2at - 3${{bt}^{2}}$
At t=2 sec , v = 4a- 12 b m/s