Question : The position vector of a particle moving in the x-y plane at any time t is given by x=(3t2-6t)m, y=(t2-2t)m. Select the correct answer
a)velocity is zero at t=0
b) acceleration is zero at t=0
c) velocity is zero at t=15
d) velocity and acceleration are never zero
Doubt by Aanshika
Solution :
x=(3t2-6t)
y=(t2-2t)
We know, V = dx/dt
Vx = d(3t2-6t)/dt = (6t-6) m/s
Vy = d(t2-2t)/dt = (2t-2) m/s
and A= dv/dt
Ax = dVx/dt = d(6t-6)/dt = 6 m/s2
Ay = dVy/dt = d(2t-2)/dt = 2 m/s2
As you can see that both velocity and acceleration are never equal to zero.
so d) is the correct option.