# General Kinematics of a Moving Body

• A particle is there which is having negligible dimension
• A body in that which is having countable dimension.
• Distance is the actual path covered by the body where as displacement is change in the initial and final position with direction.
• Distance is a scalar and displacement is a vector.
• Speed is defined as the rate of distance travelled by the body.
• Velocity is the rate of displacement of the body.
• Speed and velocity have same units and dimension
• If a particle travels first half of distance with speed V1 and rest half with speed V2 Then average speed=\tt \frac{2V_{1}V_{2}}{V_{1}+V_{2}}
• If a particle travels first half of time with speed V1 and rest half with speed V2 The average speed = \tt \frac{V_{1}+V_{2}}{2}
• For round in P average velocity = 0 Average speed > O.
• In uniform motion average velocity and instantaneous velocity are equal
• Moving with uniform acceleration a body crosses two points with velocities \tt \overline{u} \ and \ \overline{V} Then the velocity at mid point is \tt \sqrt{\frac{u^{2}+v^{2}}{2}}
• A Particle travel along a circular path making an angle ‘θ’. Then Displacement = \tt \frac{2R\ \sin \theta}{2}

### View the Topic in this video From 0:50 To 57:18

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1. Speed (v) =\tt \frac{Distance\ travelled(s)}{Time\ taken(t)}

2. Average speed = \tt \frac{Total\ distance\ travelled}{Total\ time \ taken}

3. If a particle travels distances s1, s2, s3, .... with speeds v1, v2, v3 ,...., then
Average speed = \frac{S_{1}+S_{2}+S_{3}+...}{\left(\frac{S_{1}}{v_{1}}+\frac{S_{2}}{v_{2}}+\frac{S_{3}}{v_{3}}+...\right)}

4. If particle travels equal distances (s1 = s2 = s) with velocities v1 and v2, then,
Average speed = \frac{2v_{1}v_{2}}{\left(v_{1}+v_{2}\right)}

5. If a particle travels with speeds v1, v2, v3,.... during time intervals t1, t2, t3,...., then
Average speed = \frac{v_{1}t_{1}+v_{2}t_{2}+v_{3}t_{3}+...}{t_{1}+t_{2}+t_{3}+...}

6. If particle travels with speeds v1 and v2 for equal time intervals, i.e. t1 = t2 = t, then
Average speed = \frac{v_{1}+v_{2}}{2}

7. When a body travels equal distance with speeds V1 and V2, the average speed (v) is the harmonic mean of two speeds.
\frac{2}{v}=\frac{1}{v_{1}}+\frac{1}{v_{2}}

8. Instantaneous speed = \tt \lim_{\Delta t \rightarrow 0}\ \frac{\Delta s}{\Delta t}=\frac{ds}{dt}

9. \tt velocity=\frac{Displacement}{Time\ taken}

10. \tt Average\ velocity=\frac{Total\ Displacement}{Total\ Time\ taken}

11. Instantaneous velocity: The velocity of a body at a given instant of time during motion is known as instantaneous velocity i.e.,
Instantaneous velocity =\tt \lim_{\Delta t \rightarrow 0}\frac{\Delta\overrightarrow{r}}{\Delta t}=\frac{d\overrightarrow{r}}{dt}