00:01
Given position of particle on x -axis, we defined as function of time 4 minus 2070 plus t cube.
00:11
Here, first of all, we have to find the velocity function in terms of time, which is velocity we know that is the change in distance with upon time or you can say rate of change of distance.
00:27
So if we have to do the differentiation, then putting up values, 27t plus t cube.
00:36
Now we know that differentiation for, let's say, t -raised to power n, then it will be, which is n, t, n minus 1.
00:47
This is the formula.
00:49
Now we write it here as that is t -raised to power 0.
00:53
So let's apply that then 4.
00:57
0 into t 0 minus 1 minus 27 and then 1 t 1 minus 1 minus 1 and then plus 3 t 2 minus 1 so further upon calculating this is what 0 so that term comes out to be 0 minus 27 into 1 and then t 10 10 is what 1 itself then plus 3 t raised to power 1 so that comes out to be velocity which is minus 27 plus 3 t right this is the velocity now for acceleration which is further rate of change of velocity so further putting up again value t by d t which is my minus 27 now it will be t raised to power 0 can be written then 3 t to power 1 again applying same formula minus 27 0 t 0 minus 1 plus 3 1 t 1 minus 1 and then upon solving this we've got it as 27 into 0 plus 3 and then t as to power 1 minus 1 0 itself only 1 so acceleration comes out to be 3 if we are talking about units, then it will be meter per second and that will be meter per second square...