On the particle displacement-time graph x=3sin(pie/8)t in units of centimetres and seconds. Find the first two times when the displacement is maximum
Thanks for any help
Hello,Originally Posted by nath_quam
1. Derivate x(t) with respect to t:
You'll get a maximum if dx/dt = 0 and the 2nd derivative is negative:
dx/dt = 0 if
That means t = 4*(2k+1)
You'll get a maximum if k = 1, 3, 5, ... (Use the 2nd derivative to sort these numbers out!)
So the first 2 maxima ar at t = 4 or t = 20. (See attachment)
Greetings
EB
The solution probably depends on if you are doing Math or Physics. It sounds like a Physics problem, so I'd say t=4, 12. If it's a Math problem I'd say it's t=4, 20. (Physics is a lot more liberal in it's terms: maximum displacement implies largest distance from the origin in any direction, though that's not what the Mathematical definition of it would be.)
-Dan