Question

The displacement (x) of a particle depends on time (t) as x = αt2 - βt3 .then,αβ

• A. (A) the particle will return to its starting point after time α/β
• B. (B) the particle will come to rest after time 2 α/3β
• C. (C) the initial velocity of the particle was zero but its initial acceleration was not zero
• D. (D) no net force will act on the particle at t = α/3β

Answer 1

Answer: (D)

(D) no net force will act on the particle at t = α/3β

Answer 2

Explanation:
x=αt2−βt3At t=0,x=0Particle will come to its initial position when x=0 againαt2−βt3=0⇒t=αβVelocity of the particlev=dxdt=2at−3βt2At t=0,v=0So, we can say that object is at rest initially.Velocity will be zero when2at−3βt2=0⇒t=2α3βAcceleration of the particlea=dvdt=2α−6βtAt t=0a=2αAcceleration of the particle will be zero.a=2α−6βt=0⇒t=α3βWhen the acceleration =0, force acting on it will be zero.