Question

Kinametical equation in vector form

Answer 1

The velocity, acceleration and position vectors are defined in terms of each otheras follows:$$\vec{v} = \frac{d\vec{x}}{dt}\tag{1}$$$$\vec{a} = \frac{d\vec{v}}{dt}\tag{2}$$Using the previous two, you can obtain the third differential equation:$$\vec{a} = \vec{v}\frac{d\vec{v}}{d\vec{x}} \tag{3}$$We can rearrange the equations to obtain the following:$$d\vec{x} = \vec{v} \space dt \tag{4}$$$$d\vec{v} = \vec{a} \space dt \tag{5}$$$$\vec{a}\space d\vec{x} = \vec{v}\space d\vec{v} \tag{6}$$The equations $(1), (2), (3), (4), (5)$ and$(6)$ always hold true.