Question

The velocity of a particle moving along a line is t2 - 2t sin(t2 ) meters per second. The net change in the particle's position during the time interval 0 ≤ t ≤ 4 is given by:

Answer 1

@saifoo.khan

Answer 2

@jdoe0001

Answer 3

If the time derivative of a position-time graph gives velocity, then the integral (i.e. area under the curve) of a velocity-time graph gives position as a function of time.

Answer 4

So what are your limits of integration ? Hint: the question tells you...

Answer 5

(4,0)

Answer 6

sorry (0,4)

Answer 7

Good, what are you integrating with respect to ? Is is time?

Answer 8

Velocity?

Answer 9

No. What does (0,4) represent?

Answer 10

Oh time.

Answer 11

Correct , so our differential is \[dt\] , and our limit is \[\int\limits_{0}^{4}\] . The answer should be obvious now !

Answer 12

It should be integral (0,4) t^2-2tsin(t^2) dt

Answer 13

Correct :)

Answer 14

Now if I wanted to calculate the actual net change in position to find the value in meters would I just solve the above integral?

Answer 15

Yes, that would give you the net change in position between 0 and 4 seconds.

Answer 16

Alright thank you!

Answer 17

No problem !