A particle moves in the x-y plane according to the law x=at, y=at `(1-alpha t)` where a and `alpha` are positive constants and t is time. Find the velocity and acceleration vector. The moment `t_(0)` at which the velocity vector forms angle of `90^(@)` with acceleration vector.

Explanation

`V_(x)=a, V_(y)=a-2a alphat implies vec(V)=a hat(i)+(a-2a alphat) hat(j)`
`a_(x)=0, a_(y)=-2a alpha implies vec(a)=-2 a alpha hat(j)`
for `90^(@)," "vec(V).vec(a)=0`
`2aalpha(a-2aalphat)=0`
`1-2alphat=0 implies t = 1//(2 alpha)` sec.