Question

A body of mass 4 kg moves under the action of a force F=(4i+12t^2j)N. Where t is the time taken in seconds. The initial velocity of the particle is (2i+j+2k)m/s. If the force is applied for 1s work done is?

Answer 1

Work = Force × distance.

In 1 second, the force will be:

4i + 12j + 0k, here we include k since the velocity has k and when we put zero k it does not change the value of the force.

The distance moved in one second will be :

2i + i + 2k

We see that this is a vector.

We will therefore use cross product to get the product of the two vectors.

We first write it in matrix form that is a combination of the two vectors with the leading row having I, j, k respectively.

We then find the determinant of the matrix including the leading row.

Since it forms a three by three matrix, we will use cofactor expansion to get the determinant.

When we do this we get 24i - 8j - 20k

Find calculations in the image.