Question

A person travelling on a straight line moves with a uniform velocity v1 for some time and with uniform velocity v2 for the next equal time. The average velocity v is given by
(a) v=v1+v22
(b) v=√v1v2
(c) 2v=1v1+1v2
(d) 1v=1v1+1v2

Answer 1

Explanation:

Displacement  during the velocity v_1v1 will be x_1=v_1 tx1=v1t

Displacement  during the velocity v_2v2 will be x_2=v_2 tx2=v2t

Average velocity will be \dfrac{Displacement}{time}=\dfrac{x_1 +x_2}{t+t}=\dfrac{v_1t +v_2 t}{2t}=\dfrac{v_1 +v_2}{2}timeDisplacement=t+tx1+x2=2tv1t+v2t=2v1+v2

Answer 2

Option (a)  $V =\frac{v_{1}+v_{2}}{2}$

Average velocity is given by $V =\frac{v_{1}+v_{2}}{2}$.

Explanation:                  

Given :

Two uniform velocities are $v_1$ and $v_2$.

Velocity is uniform in both cases, acceleration is 0.

We have , $\mathrm{d}_{1}=\mathrm{v}_{1} \mathrm{t}$  ( d = displacement ; t = time )

And $\mathrm{d}_{2}=\mathrm{v}_{2} \mathrm{t}$  ( d = displacement ; t = time )

Total displacement (d) can be found by adding the two displacements $d_1$ and $d_2$,    

                                          $d=d_{1}+d_{2}$

Total time (t) can be found by adding the two time, is given by

                                           t = t + t = 2 t                

Average velocity,          

                       $V=\frac{d_1+d_2}{2 t}$                        

                           $=\frac{v_{1} t+v_{2} t}{2 t}$

                           $=\frac{t\left(v_{1}+v_{2}\right)}{2 t}$

Cancel the time in the denominator and numerator.      

Average velocity  $=\frac{v_{1}+v_{2}}{2}$

Therefore, the average velocity is $\frac{v_{1}+v_{2}}{2}$.