kinematics .. how to solve this question. shouldn't acceleration be 0 when velocity is 0?

Question

a particle moves in a straight line so that , $t$ s after passing through a fixed point $O$ , its velocity $v$ in $\frac{m}{s}$, is given by $$v = 2t -11-\left(\frac{6}{(t+1)}\right)$$ Find the acceleration of the particle when it is at instantaneous rest.

Answer 1

In the following picture your problem is solved within Mathematica.The most important feature is the plot. It shows that for small positive $t$ the velocity is negative, hence the moving point moves downwards (say). But the velocity (a signed quantity!) is steadily rising, and after about $6$ seconds it is exactly zero, then becomes positive, which means that from then on the moving point begins moving upwards. Now this steadily rising of $v(t)$ is probably caused by some extraneous force. In any case the intensity of this rising of $v(t)$ is called the acceleration of the moving point, and is measured by $a(t):=v'(t)$.