Q1: A particle moves along a straight line such that distance x traversed in t seconds is given by x = t²(t + 1), the acceleration of the particle, will be

ANS:D - 6t + 2

x=t^2(t+1)=t^3+t^2.
Differentiating on both side
w.r.t. t => dx/dt=3t^2+2t then double differentiation: d^2x/dt^2=6t+2. x = t2(t+1).
x = t3+t2.

dx/dt = 3t2+2t.
d2x/dt2 = 6t+2.

This is the required answer of the acceleration but acceleration negative sign indicated.