Figures (a) and (b) show the variation of the x and y components of the acceleration with time of a particle is moving in x-y plane. At time t = 0, its velocity is v0 directed along positive y-direction. If a0=v0t0 and the angle that the velocity of the particle makes with x axis at time t = 4t0 is θ. Find the value of tan θ.

We know the area under acceleration vs. time graph gives change in velocity. It means the area under ax vs. t graph gives change in x-component of velocity (vx) ∴vx=a0t0+a0t0=2a0t0=2v0     ∵a0=v0tAlso, area under ay vs. t graph is equal to change in y-component of velocity (vy)∴ vy−v0=12×t0×a0×4=2a0t0=2v0∴ vy=3v0∴ tan⁡θ=3v02v0=1.5