If $\int_0^t \cos(f(t)) \,dt =\frac{l}{v}$ and $\int_0^t \sin(f(t))\, dt =\frac{ut}{v}$, find $t$

Question

While solving a physics problem I ended up with the following integration and I don't know how to solve it. Please help.

$$\int_0^t \cos(f(t)) \,dt =\frac{l}{v} $$

And

$$\int_0^t \sin(f(t)) \,dt =\frac{ut}{v} $$

We don't know what $f(t)$ is. We have to eliminate it and find the value of $t$ in terms of $u$, $v$ and $l$.

Note: please let me know if it is not possible to do it.

score 0 · Answer 1 · answered May 01 '19 at 06:21

0

Differentiate both sides wrt t. First equation, you get: $cos(f(t))=\frac {d(\frac l v)} {dt}$ Second equation: $sin(f(t))=\frac {d(\frac {ut} v )} {dt} $. If u,l,v are constants, then RHS reduce to 0 and u/v respectively.

answered May 01 '19 at 06:21

Tojra

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I have to find the value of t but it gets eliminated in this method. – Abhinav May 01 '19 at 06:24
Are l,u,v constants? – Tojra May 01 '19 at 06:31
Yes but we don't know f(t) – Abhinav May 01 '19 at 06:33
I think we can't find t – Tojra May 01 '19 at 06:38
I have seen the answer. $t=\frac{lv}{v^2 - u^2}$. Can this be helpful – Abhinav May 01 '19 at 06:41
May there is problem in your equations. You can post the question in physics stack exchange. Without knowledge of f, we can't find the answer. – Tojra May 01 '19 at 06:43

If $\int_0^t \cos(f(t)) \,dt =\frac{l}{v}$ and $\int_0^t \sin(f(t))\, dt =\frac{ut}{v}$, find $t$

1 Answers1