# Math Help - Mechanics problem

1. ## 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

2. $x = \frac{t^2}{2}$

$v_x = t$

$a_x = 1$

$y = 2\cos{t}$

$v_y = -2\sin{t}$

$a_y = -2\cos{t}$

$v(t) = (t)\vec{i} - (2\sin{t}) \vec{j}$

$a(t) = \vec{i} - (2\cos{t}) \vec{j}$

$|a| = \sqrt{1 + 4\cos^2{t}}$

$|a_{max}| = \sqrt{5}$ ... why?

3. graph ...