00:01
Okay, so in this question we have a source of proton which is moving along the x -axis according to the equation x equal to 50 t plus 10 t squared i know it says 10 r squared in the question, but that should be t squared.
00:12
It doesn't work if it's r squared.
00:14
So that's a typer in the question.
00:15
It should say t squared and we are asked to calculate the average velocity of the proton during the first three seconds of its motion.
00:23
Average velocity will be the distance covered in that time over what the time taken.
00:29
So for at three seconds, so x, i'll say x of three, is going to be equal to 50 multiplied by three plus 10 multiplied by three squared.
00:43
That's going to give you 150 plus 90, which is 240 meters.
00:50
It's taken three seconds to get to 240 meters, so 240 divided by three.
00:56
So distance over time will get you to average velocity.
00:59
That's going to be 80 meters per.
01:01
Second and we'll ask what's the instantaneous velocity of the proton at t's equal to three seconds so the the proton will be speeding up it will be accelerating so it's instantaneous velocity at three seconds will be greater than the average velocity so velocity is equal to the derivative or the first derivative with respect to time the x over dt that's going to be 50 multiplied by 20 t okay so we have the two here 2 times 10 is 20, so it'll be 50 plus 20 t...