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A particle moves in the x-y plane accord...

A particle moves in the x-y plane according to the law `x=t^(2)`, y = 2t. Find:
(a) velocity and acceleration of the particle as a function of time,
(b) the speed and rate of change of speed of the particle as a function of time,
(c) the distance travelled by the particle as a function of time.
(d) the radius of curvature of the particle as a function of time.

Text Solution

Verified by Experts

The correct Answer is:
(a) `veca=2hati` (b) `(2t)/(sqrt(t^(2)+1))` (c) sqrt(t^(2)+1)+In[t+sqrt(t^(2)+1)]` (d) `2(t^(2)+1)^(3//2)`
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