Finding distance from origin using acceleration

[Entr0py]

Homework Statement

Acceleration of a particle that begins at rest at the origin is given by a(t)=3ti+4tj, where a is in m/s^2 and t is in seconds. The particle's distance from the origin at time t=2s is what?

Homework Equations

You need to find velocity then distance

The Attempt at a Solution

To find velocity I integrated the acceleration (I haven't covered integration in calculus yet, so it's a bit difficult to do). I got v(t)=(3t^2)/2i+2t^2j. Now to find distance I integrate velocity. I got x(t)=(t^3)/2i+(2t^3/3)j. Plugging in t=2 s, I get x=9.33 m. But my teacher says the answer is about 7 m.

 

[gneill]

To find velocity I integrated the acceleration (I haven't covered integration in calculus yet, so it's a bit difficult to do). I got v(t)=(3t^2)/2i+2t^2j. Now to find distance I integrate velocity. I got x(t)=(t^3)/2i+(2t^3/3)j. Plugging in t=2 s, I get x=9.33 m. But my teacher says the answer is about 7 m.

You did fine with your integrations! But note that the result is a vector value with i and j components (or x and y components if you wish). How do you find the magnitude of a vector?

 

[Entr0py]

You would do the square root of the i and j hats right?

 

[Entr0py]

You did fine with your integrations! But note that the result is a vector value with i and j components (or x and y components if you wish). How do you find the magnitude of a vector?

And thank you for your response.

 

[gneill]

You would do the square root of the i and j hats right?

Square root of the sum of the squares. Like finding the hypotenuse of a right angle triangle. This is also called "adding in quadrature" if you're interested in the lingo.

 

[Entr0py]

Thank you man. I found the distance by finding the i and j hat separately. I got 4ti+(16/3)tj m. I plus in t=2 s and I get square root of 44.4. which is about 6.67 which is close to 7 m. Thanks a lot for helping me.

 

[Entr0py]

Square root of the sum of the squares. Like finding the hypotenuse of a right angle triangle. This is also called "adding in quadrature" if you're interested in the lingo.

You already know I'm interested in the lingo.