## Motion in a Straight Line

# 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 V
_{1}and rest half with speed V_{2}Then average speed=\tt \frac{2V_{1}V_{2}}{V_{1}+V_{2}} - If a particle travels first half of time with speed V
_{1}and rest half with speed V_{2}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 s_{1}, s_{2}, s_{3}, .... with speeds v_{1}, v_{2}, v_{3 },...., 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 (s_{1} = s_{2} = s) with velocities v_{1} and v_{2}, then,

Average speed = \frac{2v_{1}v_{2}}{\left(v_{1}+v_{2}\right)}

5. If a particle travels with speeds v_{1}, v_{2}, v_{3},.... during time intervals t_{1}, t_{2}, t_{3},...., 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 v_{1} and v_{2} for equal time intervals, i.e. t_{1} = t_{2} = t, then

Average speed = \frac{v_{1}+v_{2}}{2}

7. When a body travels equal distance with speeds V_{1} and V_{2}, 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}