Answer: 1 m/s
Explanation:
We have an object whose position 
is given by a vector, where the components X and Y are identified by the unit vectors 
and 
(where each unit vector is defined to have a magnitude of exactly one):
![r=[2 m + (2 m/s) t] i + [3 m - (1 m/s^{2})t^{2}] j](https://tex.z-dn.net/?f=r%3D%5B2%20m%20%2B%20%282%20m%2Fs%29%20t%5D%20i%20%2B%20%5B3%20m%20-%20%281%20m%2Fs%5E%7B2%7D%29t%5E%7B2%7D%5D%20j)
On the other hand, velocity is defined as the variation of the position in time:
This means we have to derive :
![\frac{dr}{dt}=\frac{d}{dt}[2 m + (2 m/s) t] i + \frac{d}{dt}[3 m - (1 m/s^{2})t^{2}] j](https://tex.z-dn.net/?f=%5Cfrac%7Bdr%7D%7Bdt%7D%3D%5Cfrac%7Bd%7D%7Bdt%7D%5B2%20m%20%2B%20%282%20m%2Fs%29%20t%5D%20i%20%2B%20%5Cfrac%7Bd%7D%7Bdt%7D%5B3%20m%20-%20%281%20m%2Fs%5E%7B2%7D%29t%5E%7B2%7D%5D%20j)
This is the velocity vector
And when 
the velocity vector is:
This is the velocity vector at 2 seconds
However, the solution is not complete yet, we have to find the module of this velocity vector, which is the speed 
:
Finally:
This is the speed of the object at 2 seconds
when the apple moves in a horizontal circle, the tension force in the string provides the necessary centripetal force to move in circle. the tension in the string is given as
T=mv²/r
where T = tension force in the string , m = mass of the apple
v = speed of apple , r = radius of circle.
clearly , tension force depends on the square of the speed. hence greater the speed, greater will be the tension force.
at some point , the speed becomes large enough that it makes the tension force in the string becomes greater than the tensile strength of the string. at that point , the string breaks
The two forces should be equal therefore:
2.10 * Fa = Fa + 2 * F * cos 18
simplifying the right side:
2.10 * Fa = Fa + 1.902 * F
1.10 Fa = 1.902 F
<span>F / Fa = 0.578</span>
