First slide

The two types of acceleration

Question

A particle moves on a circle of radius r with centripetal acceleration as function of time as a_e = k²rt²where k is a positive constant. Find the resultant acceleration.

Moderate

A

kt²
B

kr
C

$\large kr\sqrt {{k^2}{t^4} + 1}$
D

$kr\sqrt {{k^2}{r^4} - 1}$

Solution

$\large a_c=k^2rt^2=\frac{v^2}{r};v=krt;a_t=\frac{dv}{dt}=kr\\\\ a_{net}= \sqrt{a_c^2+a_t^2}=\sqrt{k^4r^2t^4+k^2r^2}=kr\sqrt{k^2t^4+1}$

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