Question

write the general expression of v and a (velocity & acceleration) in 3 dimension.​

Answer 1

Given that,

Velocity = v

Acceleration = a

We know that,

Velocity :

Velocity of the particle is rate of change of position of the particle.

In mathematically form,

$v=\dfrac{dx}{dt}$

Where, v = velocity

x = position of particle

t = time

The velocity in three dimension is

$\vect{r}=xi+yj+zk$

$\dfrac{dr}{dt}=\dfrac{dx}{dt}i+\dfrac{dy}{dt}j+\dfrac{dz}{dt}k$

$v=v_{x}i+v_{y}j+v_{z}k$

Acceleration :

Acceleration of the particle is rate of change of velocity of the particle.

In mathematically form,

$a=\dfrac{dv}{dt}$

Where, a = acceleration

v =velocity of particle

t = time

The acceleration in three dimension is

$\vect{v}=v_{x}i+v_{y}j+v_{z}k$

$\dfrac{dv}{dt}=\dfrac{dv_{x}}{dt}i+\dfrac{dv_{y}}{dt}j+\dfrac{dv_{z}}{dt}k$

$a=a_{x}i+a_{y}j+a_{z}k$

Hence, This is required solution.