Change in Momentum using Vectors

[Priyadarshini]

Homework Statement

A force F = (2ti + 3t^2j) N acts on an object moving in the xy plane. Find the magnitude of change in momentum of the object in time interval t=0 to t=2
(The bold ones are vectors)

Homework Equations

Ft=change in momentum

The Attempt at a Solution

magnitude of F = (4t^2 + 9t^4)^(1/2)
taking t^2 common:
t(4+9t^2)^(1/2)
Ft=delta p
so, delta p = 2t(4 + 9t^2 ) ^ (1/2)

But the answer doesn't have ts in it.

 

[Fightfish]

Have you learned calculus? The force is time-dependent, so you will have to perform an integration to find out the total change in momentum over the time interval.

 

[Priyadarshini]

Have you learned calculus? The force is time-dependent, so you will have to perform an integration to find out the total change in momentum over the time interval.

I have learned it. But have never actually used it in physics.
So I integrate F?
Like:
Integration of 2ti+3t^2 j
is t^2i + t^3j
with the limits 0 and 2
Then,
4i + 8j is the change in p

 

[Fightfish]

Yes. You can understand the integration process by looking at Newton's second law, which states that $$\vec{F} = \frac{d\vec{p}}{dt}$$, and so this immediately results in $$\Delta p = \int_{t_0}^{t_f}\vec{F} dt$$

 

[Priyadarshini]

Yes. You can understand the integration process by looking at Newton's second law, which states that $$\vec{F} = \frac{d\vec{p}}{dt}$$, and so this immediately results in $$\Delta p = \int_{t_0}^{t_f}\vec{F} dt$$

Thank you!