00:01
In this question, we are given a particle's velocity function and its position after 25 seconds.
00:07
And we are asked to find the general position function.
00:11
And to do that, to find the position function, we need to integrate the particle's velocity function.
00:19
So we need to calculate the integral of 1 .5 square root of t d t .t.
00:28
To apply the power rule, we will rewrite the square root of t as t to the one -half power.
00:36
Now, by the power rule, this integral equals to t to the three -half divided by 3 over 2, plus the constant of integration c.
00:48
Now, recall that 1 .5 is also 3 over 2.
00:53
So it's 3 over 2 times 2 over 3 times t to the 3 over 2 plus c.
01:00
3 over 2 and 2 over 3 -over 3 cancel each other, and we are going to get t to the 3 -5s plus c is the particle's position function.
01:09
However, we haven't found c yet.
01:13
To find c, we will use this condition...