Suppose the pickpocket is caught at a time t after the motorcycle starts.The distance travelled by the motorcycle during this interval is
.
`s=1/2 at^2` ...........i.
During this interval the jeep travels a distance
`s+d=vt.` ............ii
By i. and ii.
`1/2 at^2-vt+d=0`
`or , t=(v+-(sqrt(v^2-2ad)/a`
Thie pickpocket will becaught if t is real and positive.
This will be possible if
`v^2ge2ad or, vgesqrt(2ad)`