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2.Motion in Straight Line
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The acceleration of a particle starting from rest, varies with time according to the relation $A = -a\omega^2 sin\omega t.$ The displacement of this particle at a time $t$ will be
A
$ - \frac{1}{2}\,(a{\omega ^2}\sin \omega \,t)\,{t^2}$
B
$a\omega \,\sin \omega \,t$
C
$a\omega \,\cos \omega \,t$
D
$a\,\sin \omega \,t$
Solution
(d) Velocity $v = \int {A\;dt = \int {( – a{\omega ^2}} } \sin \omega t)\;dt = a\omega \cos \omega t$
Displacement $x = \int {v\;dt = \int {a\omega } } \cos \omega t\;dt = a\sin \omega t$
Standard 11
Physics
