Answer: amplitude
Explanation: This describes the maximum amount of the displacement of a particle from it rest position. Usually, it is measured in metres
Since we are considering AM which is amplitude modulation, a technique used in electronic communication, most commonly for broadcasting information through a radio carrier wave. In amplitude modulation, the amplitude (signal strength) of the carrier wave is diversified in proportion to that of the message signal being broadcasted.
Answer:
The new force becomes 4 times the initial force.
Explanation:
The force of attraction or repulsion is given by the relation as follows :

Where
d is the distance between the interacting charges
F is inversely proportional to the distance between charges.
If the distance is halved, d'=(d/2), new force is given by :

So, the new force becomes 4 times the initial force.
Answer:
W=315 x 10⁵ J
Explanation:
Given that
F= 2.5 x 10⁵ N
d= 90 m
K.E.=5.4 x 10⁷ J
We know that work done by all force is equal to the change in kinetic energy
Lets take work done by catapult is W
W + F.d= K.E.
W= 5.4 x 10⁷ - 2.5 x 10⁵ x 90 J
W= (540 - 25 x 9) 10⁵ J
W=315 x 10⁵ J
Explanation:
It is given that, the position of a particle as as function of time t is given by :

Let v is the velocity of the particle. Velocity of an object is given by :

![v=\dfrac{d[(8t+9)i+(2t^2-8)j+6tk]}{dt}](https://tex.z-dn.net/?f=v%3D%5Cdfrac%7Bd%5B%288t%2B9%29i%2B%282t%5E2-8%29j%2B6tk%5D%7D%7Bdt%7D)

So, the above equation is the velocity vector.
Let a is the acceleration of the particle. Acceleration of an object is given by :

![a=\dfrac{d[8i+4tj+6k]}{dt}](https://tex.z-dn.net/?f=a%3D%5Cdfrac%7Bd%5B8i%2B4tj%2B6k%5D%7D%7Bdt%7D)

At t = 0, 

Hence, this is the required solution.