Question

the velocity vector at a point A varies with time as v=ai+btj where a and b are positive constants. the equation of trajectory of the point would be?​

Answer 1

Answer:

The velocity vector at a point A varies with time as v=ai+btj where a and b are positive constants.

Explanation:

v=ai+btj

So, dx/dt= a dy/dt = bt..........(1)

From (1)  ∫dx= a∫dt

or, x = at............(2)

and dy= bt dt= bat dt

integrating ∫ dy= ab ∫  t dt

or, y= 1/2 ab t^2...............(3)

from (2) and (3) we get y= b/2a x^2

Answer 2

Please check the attachment