00:01
In this problem, it is stated that the acceleration function in meter per second square and initial velocity are given for a particle moving along a line.
00:13
Find the velocity at time t and the distance travel during the given time interval.
00:18
So we are more interested in finding velocity and distance.
00:23
So can we are having this function, right? so let us take at is actually acceleration which is given by function t plus 4.
00:37
And b0, v at 0 seconds you can say is actually 5.
00:44
And we are given with the intervals.
00:46
0 is less than or equals to t, less than or equals to 10.
00:49
So the interval lies between 0 to 10.
00:53
All right.
00:55
So acceleration is actually given by the differentiation of velocity, with respect to time and velocity is actually given by the differentiation of displacement with respect to time.
01:10
So these both are very important thing which we are going to follow now.
01:18
Or you can also reverse it and if we want to find velocity from the acillitation then we will just integrate it.
01:25
Okay.
01:27
Similarly for displacement if we want to find the displacement then we will just integrate the velocity.
01:35
Of velocity so now we are given a t plus 4 so can we write it like this a t d t this is integration from a to b let us say this is a to v this is the interval right and this is actually equal to v t okay so this will give us v t is actually equal to the of you can say a to b, a is zero...