Question

a body is travelling between 2 positions travels for time interval t1 t2 t3..tn with speeds v1 v2 v3..vn respectively what is average speed of total motion​

Answer 1

Answer:

math]v=\dfrac{s}{t}\implies t=\dfrac{s}{v}\tag*{}[/math]

The time intervals are, therefore,

[math]t_1=\dfrac{s}{v_1}\tag*{}[/math]

[math]t_2=\dfrac{s}{v_2}\tag*{}[/math]

[math]t_3=\dfrac{s}{v_3}\tag*{}[/math]

The average speed is given by,

[math]\langle v\rangle=\dfrac{\text{ Total Distance}}{\text{Total Time}}\tag*{}[/math]

[math]\langle v\rangle =\dfrac{s+s+s}{\frac{s}{v_1}+\frac{s}{v_2}+\frac{s}{v_3}}\tag*{}[/math]

[math]\langle v\rangle=\dfrac{3s}{s(\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}}\tag*{}[/math]

[math]\langle v\rangle=\dfrac{3}{\frac{1}{v_1}+\frac{1}{v_2}+\frac{1}{v_3}}\tag*{}[/math]

[math]\boxed{\langle v\rangle =\dfrac{3v_1v_2v_3}{v_1v_2+v_2v_3+v_3v_1}}\tag*{}[/math]