Question

A force F = (3x2 + 2x + 1) N (where x is in metre) is acting on a body of mass 10 kg. The change in kinetic energy of the body when it moves from A (0,1,2) m to B (2, 0, 3) m, will be​

Answer 1

Answer:

8J

Explanation:

I have attached my answer , let me know if it is correct or not.

Answer 2

Given:

A force F = (3x2 + 2x + 1) N (where x is in metre) is acting on a body of mass 10 kg.

To find:

Change in KE ?

Calculation:

It is best to apply Work-Energy Theorem:

• The work done by all the forces on the object will be equal to the change in kinetic energy of the object.

$\rm \: W = \Delta KE$

$\rm \implies \displaystyle \: \int F \times dx\: = \Delta KE$

$\rm \implies \displaystyle \: \Delta KE = \int \: (3 {x}^{2} + 2x + 1) \: dx$

Putting limits:

$\rm \implies \displaystyle \: \Delta KE = \int_{0}^{2} \: (3 {x}^{2} + 2x + 1) \: dx$

$\rm \implies \displaystyle \: \Delta KE = \bigg \{ {x}^{3} + {x}^{2} + x \bigg \}_{0}^{2}$

$\rm \implies \displaystyle \: \Delta KE = {2}^{3} + {2}^{2} + 2$

$\rm \implies \displaystyle \: \Delta KE = 14 \: joule$

So, change in kinetic energy is 14 joule.