Q. 32 Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions.

If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.


Hint: Velocity, v= dxdt and Acceleration, a = dvdt
Step 1: Find acceeration along x-axis.

Clearly, from diagram (a), the variation can be related as

x=tdxdt=1m/sax=0

Step 2: Find acceleration along the y-axis.

Fromdiagramby=t2dydt=2t or ay=d2ydt2=2m/s2Step3:FindnetforceHence,Fy=may=500×103×2=1Nm=500gFx=max=0Hence,netforce,F=Fx2+Fy2=Fy=1Nalongy-axis