This time it's a Rocket
The velocity of a rocket is given by the following function:
Find the displacement of the rocket over the time interval .
Image credit: Wikimedia Commons .
The answer is 16.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Moderator note:
Simple standard approach.
We know that the area under the velocity time graph gives us the displacement traversed in that interval. And we know that this is nothing but the integral of the velocity function over that period.
Thus the displacement of the rocket over the time interval ( 1 , 3 ) will be:
∫ 1 3 3 x 2 − 2 x − 1 d t = [ x 3 − x 2 − x ] 1 3 = 3 3 − 3 2 − 3 − ( 1 3 − 1 2 − 1 ) = 2 7 − 9 − 3 + 1 = 1 6
Thus the displacement of the rocket is 1 6 m .