The equation of motion of a particle is s = t3 − 3t, where s is in meters and t is in seconds. (assume t ≥ 0.) (a) find the velocity and acceleration as functions of t. g

Explanation:

The  equation of motion of a particle is :

Where

s is in meters

t is in seconds

The position of a particle is,

The acceleration of a particle is,

Hence, this is the required solution.

Velocity: m/s

Accelaration: m/s²

Explanation:

The velocity is the derivative of the position.

The accelaration is the derivative of the velocity.

Derivative concepts

The derivative of is

The derivative of a subtraction is the subtraction of the derivatives.

The derivative of a constant is 0.

The equation of the position is

m

The equation of the velocity is

Derivative of the position

m/s

The equation of the acceleration is

m/s²

a.   mass number from atomic number

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.