Thread: Mechanics problem

Hi,

Could anybody help with this one please:

Q. A point particle moves in a plane with trajectory (in metres per second)

→
r (t) = x(t)i + y(t) j,

where

x(t) = 1/2 t²

y(t) = 2 cos(t)

a) Sketch the trajectory of the particle for t ≥ 0. (not sure if you can do this on a msg board!).

b) Compute the velocity,
→
v(t), of the particle for t ≥ 0.

c) Compute the acceleration,
→
a (t), of the particle for t ≥ 0 and determine the maximum value of the magnitude of the vector
→
a (t).

I know the velocity is the derivative and acceleration is the second derivative but I'm not sure about magnitude, especially the max value.

Thanks

... why?

graph ...