Write an expression for component of Instantancous velocity or velocity and also define it.

Explanation

(i) The instantaneous velocity at an instant t or simply 'velocity' at an instant t is defined as limiting value of the average velocity as `Deltat rarr 0`, evaluated at time t.
(ii) In other words, velocity is equal to rate of change of position vector with respect to time. Velocity is a vector quantity.
`vecv=lim_(Deltatrarr0)(Deltavecr)/(Deltat)=(dvecr)/(dt)`
(iii) In component from, this velocity is
`vecv=(dvecr)/(dt)=(d)/(dt)(xhati+y hatj+zhatk)`
`=(dx)/(dt)hati+(dy)/(dt)hatj+(dz)/(dt)hatk`
Here `(dx)/(dt)=v_(x)=x-` component of velocity.
`(dy)/(dt)=v_(y)=y-` component of velocity.
`(dz)/(dt)=v_(z)=z-` component of velocity.
The magnitude of velocity v is called speed and is given by `v=sqrt(v_(x)^(2)+v_(y)^(2)+v_(z)^(2))`
Speed is always a positive scalar. The unit of speed is also meter per second.