Motion in Straight line - Physics Formulas
1. Distance and Displacement
Distance ≥ |displacement|
2. Speed
`\overline v=\frac{Total\ distance}{Total\ time}`
`\overline v=\int_{t_1}^{t_2}\frac{\|v\|dt}{t_2-t_1}`
3. Velocity
`\ v=\int_{t_1}^{t_2}\frac{vdt}{t_2-t_1}`
`V=\frac{dx}{dt}`
4. Harmonic mean
When object covers half distance with velocity v1 and half with velocity V2, then average speed will be
`v_{av}=\frac{2v_1v_2}{v_1+v_2}`
5. Geometric mean
When object covers half time with v1 and half time with v2, then average speed will be
`v_{av}=\frac{v_1+v_2}2`
6. Acceleration
`a=\frac{dv}{dt}=v\frac{dv}{dx}`
7. Equations of Motion
v = u + at
`V^2-u^2=2as`
`s=ut+\frac{at^2}2`
8. Relative Velocity
`V_B=V_A-V_B`
9. Velocity at mid-point (When Object is moving along straight line)
`v_{mid\pt}=\sqrt{\frac{v_A^2-v_B^2}2}`
10. When body is accelerate with `\alpha` and retarded with `\beta` then,
`v_{max}=\frac{\alpha\beta T}{\alpha+\beta}`
`s=\frac{\alpha\beta T^2}{2(\alpha+\beta)}`