  The position of a particle in meters is given by x =2.5t + 3.1t ^2 - 4.5t^3, where t is the time in seconds. What are the instantaneous velocity and instantaneous acceleration at t = 0.0 s? At t = 2.0 s? What are the average velocity and average acceleration for the time interval 0 greater than or equal to t less than or equal to 2.0 s?

Question

The position of a particle in meters is given by x =2.5t + 3.1t ^2 - 4.5t^3, where t is the time in seconds. What are the instantaneous velocity and instantaneous acceleration at t = 0.0 s? At t = 2.0 s? What are the average velocity and average acceleration for the time interval 0 greater than or equal to t less than or equal to 2.0 s?

Step 1

Step-1:

To determine:

The instantaneous velocity and instantaneous acceleration at t = 0.0 s. At t = 2.0 s?

The average velocity and average acceleration for the time interval  greater than or equal to t less than or equal to 2.

Given information:

The equation of position of the particle in meters is

The time interval is 2s.

Step 2

Step-2:

Formula used:

The formula to find the instantaneous velocity is,

The formula to find the instantaneous acceleration is,

The formula to find the average velocity is,

The formula to find the average acceleration is,

Step 3

Step-3:

Finding instantaneous velocity v(t) at time t=0 and t=2:

Substitute the value of x(t) ...

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