The position of an object along the x-axis is described by the formula x = 3t 2 − 2t. which of the following are the correct formulas for the velocity and acceleration of the object?

the formulas of velocity and acceleration can be given as:

Velocity :

Acceleration :

Explanation:

Given:

The position function or formula for an object along x-axis is given by:

To find the velocity and acceleration formulas.

Solution.

Velocity of an object is defined as rate of change of position of an object.

The rate of change can be found out by taking derivative of the position function of the object.

Thus the velocity formula can be written as:

      [ As and ]

So, the velocity can be represented as    

Acceleration of an object is defined as rate of change of velocity. In order to find rate of change of velocity, we will take derivative of the velocity function.

Thus the acceleration formula can be given as :

   [ As and ]

So, the acceleration can be represented as    

their final velocity is 0.091 m/s

Explanation:

Given;

mass of the first train, m₁ = 138,000 kg

mass of the second train, m₂ = 123,000 kg

initial velocity of the first train, u₁ = 0.288 m/s

initial velocity of the seocnd train, u₂ = -0.131 m/s (opposite direction to the first)

Let their common final velocity after been coupled = v

Apply the principle of conservation of linear momentum;

m₁u₁  +  m₂u₂ = v(m₁  +  m₂)

(138,000 x 0.288)    +    (-0.131 x 123,000)   =   v(138,000 + 123,000)

39,744   -   16,113   =  v(261,000)

23,631 = v(261,000)

v = 23,631 / 261,000

v = 0.091 m/s

Therefore, their final velocity is 0.091 m/s