Question

the postion x of a particle varies with time(t) as x=at^2+bt^2.the acceleration at time t of the particle will be equal to zero for which value of t?

Answer 1

\[x = a t ^{2 } + b t ^{2}\]
one can write it as
\[x = (a+b)t ^{2}\]
differentiating it with respect to t\[\frac{ dx }{ dt } = (a+b) 2t\] = speed
differentiating it again to find the acceleration
\[\frac{ d ^{2} x }{ dt ^{2} } = 2 (a+b)\]
hence the acceleration is independent of the time(t)
it can only be zero if a and b are both zero or one is aditive inverse of other