Question

the position of moving object at time t is x=2t^3 find acceleration​

Answer 1

Answer:

12t

Explanation:

To calculate the position,velocity,acceleration of any given equation.

We should actually know how to integrate and differentiate with the basic rules.

In appearance, it is a secondary school question.

Lets,discuss the basic rules to differentiate and to find the way to answer.

Given Equation :- x= 2t³

=> Position---(dx/dt)-----> velocity---(dv/dt)---> acce.

So, lets differentiate the equation to find out velocity.

=> dx/dt= d(2t³)/dt

=> dx/dt = 6t²

=> which is the velocity of particle.

Now, For acceleration,

=> dv/dt= d(6t²)/dt

=> dv/dt= 12t

which is the required acceleration after synthesis.

So, The acceleration of the object at time "t" is 12t

Ans.

Answer 2

Given: The position of moving object at time t is x = 2t³.

To find: The acceleration of the moving object.

Solution:

• Acceleration is the change in velocity of an object with respect to the time.

• Velocity of an object is the change in position of an object with respect to the time.
• The equation of the position of the object given is as,

        $x = 2t^{3}$

• According to the dimensions of acceleration, it can be given by,

        $a = \frac{x}{t^{2} }$

• Here, a is the acceleration and x is the position of the object.
• So, $a = \frac{2t^{3} }{t^{2} }$

                 $= 2t$

Therefore, the acceleration of the moving object is 2t.