00:01
In this question it is given that the equation of position that is s is a function of time t, that is s t equals to t squared minus t minus 5 power 1 by 2.
00:25
So we have to find the velocity and acceleration equation.
00:32
So we know that velocity v equals to differentiation of s with respect to time, that is ds by d t, and that is equals to 2 t minus 1 by 2 into 1 by root under t minus 5.
00:55
So this will be the equation of velocity.
01:01
Now coming to the acceleration equation, a equals to a equals to dv by d t that is differentiation of this velocity again with respect to time or double differentiation of this position equation with respect to time so when we differentiate this equation we will get 2 minus 1 by 2 into d by d t of t minus 5 power 1 by 2 so when we differentiate this, we will get, sorry, it is d, d, d, d, t minus 5, power minus 1 by 2.
01:54
Because here it is root is in denominator.
01:58
So when we go upside in the numerator, then it will become power minus 1 by 2.
02:09
So in that case when we differentiate this we will get 2 minus 1 by 2 into minus 1 by 2 into t minus 5 power 3 by 2 or minus 3 by 2.
02:27
So it will be minus 3 by 2.
02:30
So this will be the equation of acceleration.
02:35
So these are the equation of position.
02:41
This is velocity equation and this is acceleration equation.
02:49
So now coming to the question number b, that is, when is object is at rest.
02:57
So when the object will be at rest, at that point the velocity will be equals to 0...