Question

A body of mass 1 kg is acted upon by a force
F = 2 sin 3 xi +3 cos 3xj, find its position at t = 1 sec
if at t = 0 it is at rest at origin.
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Answer 1

HELLO DEAR,

GIVEN:-  

m = 1kg

F = 2sin3Πt î + 3cos3Πtj

we know:- F = ma

=> F = 1 * a

=> F = a

now,  

dv/dt = a

=> dv/dt = 2sin3Πtî + 3cos3Πtj

$\bold{\int \limits_{0}^{1} {dv}= \int \limits_{0}^{1} \{2sin3\pi \: t \; i \; + \; 3cos3\pi \: t \;j\}.dt}$

=> $\bold {\int \limits_{0}^{1} \dfrac {dx}{dt} = [\dfrac{2}{3\pi} (-\cos3 \pi \; t)i \; + \; \dfrac{3}{3\pi} (\sin3\pi \; t)j]_{0}^{^1}}$

=> $\int \limits_{0}^{1} \dfrac{dx}{dt}$ = 2/3π(-cos3π + cos0)î + 1/π(0 - 0)j

=> v = 2/3π(1 + 1)î + 1/π(0)j = dx/dt

=> x = 4/3π

and y = 0

I HOPE IT'S HELP YOU DEAR,

THANKS