Q1: The equation of motion of a particle starting from rest along a straight line is x = t³ - 3l² + 5. The ratio of the velocities after 5 sec and 3 sec will be

ANS:D - 5

x = t^3 - 3t^2 + 5 ------ Equation (A).

For Velocity V, eq. A will be.

dx / dt = V = 3t^2 - 6t ------- Equation (B).

At T1 = 5,

V1 = 3 (5)^2 - 6 (5).

V1 = 45.

& T2 = 3.

V2 = 3 (3) 2 -6 (3).

V2 = 9.

V1/V2 = 45/9 = 5.