
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 tē
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

$\displaystyle x = \frac{t^2}{2}$
$\displaystyle v_x = t$
$\displaystyle a_x = 1$
$\displaystyle y = 2\cos{t}$
$\displaystyle v_y = 2\sin{t}$
$\displaystyle a_y = 2\cos{t}$
$\displaystyle v(t) = (t)\vec{i}  (2\sin{t}) \vec{j}$
$\displaystyle a(t) = \vec{i}  (2\cos{t}) \vec{j}$
$\displaystyle a = \sqrt{1 + 4\cos^2{t}}$
$\displaystyle a_{max} = \sqrt{5}$ ... why?
