Suppose you are building a sequence consisting of 0 and 1 in such a way that:
- you start with 1
- no consecutive 0s are allowed
Examples of such sequences are: 1, 1010, 110111101 etc. Empty sequence is also allowed.
I want to prove by induction that the number of 0s in such a sequence is...
Thanks,
let me try to solve now...
\frac{ds}{1+{s}^2}=dt
\int\frac{ds}{1+{s}^2}=\int dt
\arctan s=t
s(t)=\tan t
Now
v(t)=\frac{ds}{dt}=\frac{\tan t}{dt}=\frac{1}{{\cos}^{2}t}
This is strange, because it seems that velocity is practically infinity at point t = pi/2.
I am aware of that..
But the problem is that am not so much familiar with calculus and when it comes to physics I don't know what to do when integrating/differentiating some functions which is dependent on many variables...
The first things that bothers me is whether it is correct that...
I have spent a long time stuggling with an interesting problem which was set up by my brother some time ago:
Consider an object that starts moving along the line according to the equation below:
v(s)=1+{s}^{2}
where s is the total distance traveled by the object and v is the velocity of the...
I wonder how could I calculate impact force of an object (eg. a stone) in a free fall impacting on the perfectly inelastic (perfectly hard) floor.
I know:
- m -mass of the falling object
- h -height of the fall
- v -speed at the time of impact
- t -time it...