CBSE-XI-Physics
03: Rest and Motion: Kinematics
- #5A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocityv2 for the next equal distance. The average velocity v is given by
-(a)
v=v1+v22
(b)
v=v1v2
(c)
2v=1v1+1v2
(d)
1v=1v1+1v2digAnsr: cAns : (c) `` \frac{2}{v}=\frac{1}{{v}_{1}}+\frac{1}{{v}_{2}}``
Velocity is uniform in both cases; that is, acceleration is zero.
`` x={v}_{1}{t}_{1}\Rightarrow {t}_{1}=\frac{x}{{v}_{1}}``
`` x={v}_{2}{t}_{2}\Rightarrow {t}_{2}=\frac{x}{{v}_{2}}``
Total displacement, `` x\text{ ' }=2x``
Total time, `` t={t}_{1}+{t}_{2}``
`` \therefore `` Average velocity, `` v=\frac{x\text{ ' }}{t}=\frac{2{v}_{1}{v}_{2}}{{v}_{1}+{v}_{2}}``
`` \Rightarrow \frac{2}{v}=\frac{1}{{v}_{1}}+\frac{1}{{v}_{2}}``