Answer to Question #135487 in Mechanical Engineering for Fredrick Moleleki

Question

A particle moves in a straight line such that the velocity is 5 + 3cosX. Given that the displacement is zero when the time is zero , find an expression of time as a function of the displacement

Answer 1

$v=5+3\cdot\cos x\to \frac{dx}{dt}=5+3\cdot\cos x\to$

$dt=\frac{1}{5+3\cdot\cos x}dx\to$

$\int dt=\int \frac{1}{5+3\cdot\cos x}dx$ $\to t=\frac{tan^{-1}(\frac{\tan(x/2)}{2})}{2}+C$

if $x=0$ then $t=0\to C=0$

So,

$t=\frac{tan^{-1}(\frac{\tan(x/2)}{2})}{2}$ . Answer