Seriously? You have done the hard part! The speed at time t= 10 is just the length of the velocity vector at t= 10. Replace t with 10, calculate the velocity vector and the find its length.
I'm trying to do some revision before classes start again tomorrow but I'm struggling a little bit with this one, any help would be greatly appreciated! I've included my working so far:
A particle moves in 2D with a vector velocity which at time t is ' v = (-0.4ti + 5j) m/s '.
At time t=0 the particle is at (3,2)
a) Find the acceleration vector at time t
b) Find the position vector at time t
c) Find the speed at time t = 10
I found the acceleration vector at time t to be -0.4i m/s^2
I can't figure out how to find the position vector at time t and also not sure how I'd carry on to do part c.
I've integrated to get: 'r = -0.2t²i + 5tj + c' and i know at time t=0, 'r = 3i + 2j' but I'm not sure what to do to finish off the question. Thank you for any help!
edit: I found b) to be 'r = (3-0.2t²)i + (5t+2)j' but I was wondering if anybody could still help me with c)?
Yeah, sorry! I was a bit of an idiot and wrote the wrong bit down I was stuck on.... I got the speed to be 9 m/s.
The bit I was stuck on was 'Find the time at which it crosses the Y-axis'
I'm such an idiot!! Thank you for the help on that one anyway!