a particle moves in a straight line so that , t s after passing through a fixed pointO , its velocity, v m/s, is given by v=2t-11-(6/(t+1)). find the acceleration of the particle when it is at instantaneous rest.
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 $a(t):=v'(t)$.