Linear Speed Formula

Linear speed is the measure of the concrete distance travelled by a moving object. The speed with which an object moves in the linear path is termed linear speed. In easy words, it is the distance covered for a linear path in the given time.

Linear Speed Formula is articulated as:

\(\begin{array}{l}v=\frac{\bigtriangleup s}{\bigtriangleup t}\end{array} \)


the distance travelled is s and
the time taken is t

Linear Speed Formula in the sense of angular speed is articulated as

v = ωr


the angular speed is ω  and
the radius of the circular path is r

The Linear speed formula is made use of to compute the linear speed of any given object if its angular velocity and radius of the circular path are provided. Linear speed is articulated in meter per speed (m/s).

Solved Examples

Underneath are some problems based on linear speed which may be helpful for you.

Example 1: A body starting from rest moves with the acceleration of 5 rad s-2 in a circle of radius 3m. Compute the linear speed after 5 s.

Acceleration a = 5 rad s-2

Radius r = 3 m

Time t = 5 s

The angular velocity is given by

ω = ω0 + at

= 0 + 5(5)

= 25 rads-1

The linear speed is given by

v = r ω

= 3 m × 25 rad s-1

v= 75 m/s.

Example 2: Compute the linear speed of a body moving at 50 rpm in a circular path having a radius of 2 m?



Angular  velocity = 50 rpm

\(\begin{array}{l}50 \times \frac{\pi }{30}\end{array} \)

ω = 5.237 rad/s

Radius r = 2 m

The linear speed is given by

v = r ω

v = 2 m × 5.237 rad/s

v = 10.473 m/s

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