A particle is moving in x-y plane. At certain instant of time, the components of its velocity and acceleration are as follows: vx=3m/s,vy=4m/s,ax=2m/s2 and ay=1m/s2. Find the rate of change of speed (in m/s2) at this moment.

Instantaneous speed of particle isv=vx2+vy2 or v2=vx2+vy2              ………. (1)Differentiating (1) with respect to time we get:2v⋅dvdt=2vxdvxdt+2vy⋅dvydtor dvdt=vxax+vyayvor rate of change of speed dvdt=vxax+vyayvx2+vy2substituting the given values, we get dvdt=2 m/s2