MHT CET202522 Apr 2025Evening ShiftPhysicsMotion in One DimensionActual
At any time ' t ', the co-ordinates of moving particle are x=a t^2 and y = bt ^2 . The speed of the particle is
Options
- A2 t a^2+b^2
- B2 t a^2-b^2
- C2 t(a+b)
- D2 t a ^2+ b ^2
Correct answer
A. 2 t a^2+b^2
Step-by-step solution
The position of the particle at time t is defined by x = at^2 and y = bt^2 . Differentiating both coordinates with respect to time, the velocity components are v_x = 2at and v_y = 2bt . The speed is the magnitude of the velocity vector: v = v_x^2 + v_y^2 = (2at)^2 + (2bt)^2 = 4a^2t^2 + 4b^2t^2 = 4t^2(a^2 + b^2) = 2t a^2 + b^2 . This result corresponds to option A. A