Answer
given,
position of particle
x(t)= A t + B t²
A = -3.5 m/s
B = 3.9 m/s²
t = 3 s
a) x(t)= -3.5 t + 3.9 t²
velocity of the particle is equal to the differentiation of position w.r.t. time.

------(1)
velocity of the particle at t = 3 s
v = -3.5 + 7.8 x 3
v = 19.9 m/s
b) velocity of the particle at origin
time at which particle is at origin
x(t)= -3.5 t + 3.9 t²
0 = t (-3.5 + 3.9 t )
t = 0, 
t = 0 , 0.897 s
speed of the particle at t = 0.897 s
from equation (1)
v = -3.9 + 7.8 t
v = -3.9 + 7.8 x 0.897
v = 3.1 m/s
Answer: 86.47 g of carbon-14 must have been present in the sample 11,430 years ago.
Explanation:
Half-life of sample of carbon -14= 5,730 days

Let the sample present 11,430 years(t) ago = 
Sample left till today ,N= 0.060 g

![ln[N]=ln[N]_o-\lambda t](https://tex.z-dn.net/?f=ln%5BN%5D%3Dln%5BN%5D_o-%5Clambda%20t)
![\log[0.060 g]=\log[N_o]-2.303\times 0.00012 day^{-1}\times 11,430 days](https://tex.z-dn.net/?f=%5Clog%5B0.060%20g%5D%3D%5Clog%5BN_o%5D-2.303%5Ctimes%200.00012%20day%5E%7B-1%7D%5Ctimes%2011%2C430%20days)
![\log[N_o]=1.9369](https://tex.z-dn.net/?f=%5Clog%5BN_o%5D%3D1.9369)

86.47 g of carbon-14 must have been present in the sample 11,430 years ago.
Radius of Earth is given as

now here the height from the surface of earth is same as that of radius

now here the acceleration due to gravity at this height is given as



now the force of gravity on the given object will be




<em>so the force of gravity on it is 1.225 N</em>
Answer:
The string is more likely to break when the circle is vertical
Explanation:
The string is more likely to break when the circle is vertical because tension in the string is the same throughout the circular motion and it is equal to mrw^2 when it is rotated in the horizontal plane while tension in the string is maximum and is given by mrw^2+mg when in the vertical plane.