## Linear Speed Formula :

Linear Speed Formula V _{(m/s )} in meter per second is equal to Δs_{(m)} in meter and divided by the Δt_{(s)} in second. Hence the Linear Speed Formula can be written as,

**V _{(m/s )}=Δs_{(m)}/Δt_{(s)}**

V→ velocity in m/s

Where,

The distance travelled is s in m

The time taken is t in second

##### Linear speed formula in the sense of angular speed is articulated as,

**V _{(m/s)}=r _{(cm)}*ω_{(r)}**

V→ velocity in m/s

R→ radius in cm

Where,

The angular speed is ω and

The radius of the circular path is r

## Sample Problems :

## Problem1 :

A body starting from rest moves with the acceleration of 4rad S^{-2} in a circle of radius 8m. compute the linear speed after 4s.

### Solution :

Acceleration a=4rad S^{-2}

Radius r=8m

Time t=4s

The angular velocity is given by

Ω=ω_{0}+at

=0+4(4)

=16 rads^{-1}

The linear speed is given by

V=r*ω

=8m*16 rads^{-1}

=128m/s

## Problem2 :

A body starting from rest moves with the acceleration of 9 rad S^{-2} in a circle of radius 4m. compute the linear speed after 6s.

### Solution :

Acceleration a=9rad S^{-2}

Radius r=4m

Time t=6s

The angular velocity is given by

Ω=ω_{0}+at

=0+9(6)

=54 rads^{-1}

The linear speed is given by

V=r*ω

=9m* 54 rads^{-1}

=486m/s