A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance- The average velocity v is given bya v - v 1- v 22b v-v 1 v 2c 2 v -1 v 1-1 v 2d 1 v -1 v 1-1 v 2

(c) 2v=1v1+1v2 Velocity is uniform in both cases; that is, acceleration is zero. x=v1t1 #8658;t1=xv1 x=v2t2 #8658;t2=xv2 Total displacement, x #39;=2x To ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Physics

Derivation of Velocity-Time Relation by Graphical Method

A person trav...

Question

A person travelling on a straight line moves with a uniform velocity v₁ for a distance x and with a uniform velocity v₂ for the next equal distance. The average velocity v is given by
(a) $v = \frac{v_{1} + v_{2}}{2}$
(b) $v = \sqrt{v_{1} v_{2}}$
(c) $\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$
(d) $\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

Open in App

Solution

(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, $x' = 2 x$
Total time, $t = t_{1} + t_{2}$
$∴$ Average velocity, $v = \frac{x'}{t} = \frac{2 v_{1} v_{2}}{v_{1} + v_{2}}$
$\Rightarrow \frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}$

Suggest Corrections

Similar questions

Q. 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 = \frac{v_{1} + v_{2}}{2}

(b)

v = \sqrt{v_{1} v_{2}}

(c)

\frac{2}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}

(d)

\frac{1}{v} = \frac{1}{v_{1}} + \frac{1}{v_{2}}

Q. A person traveling on a straight line moves with a uniform velocity

v_{1}

for a distance

x

and with uniform velocity

v_{2}

for the next equal time. The average velocity

v

is given by

Q. A person travelling on a straight line moves with a uniform velocity

v_{1}

for some time and with uniform velocity

v_{2}

for the next equal time. The average velocity

v

is given by:

A person travels along a straight road for half the distance with velocity $v_{1}$ and the remaining half distance with velocity $v_{2}$ The average velocity is given by

A boy runs along a straight path for the first half of the distance with a velocity $v_{1}$ and the second half of the distance with a velocity $v_{2}$ . The average velocity V is given by

Join BYJU'S Learning Program

A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 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+1v2

(c) 2v=1v1+1v2 Velocity is uniform in both cases; that is, acceleration is zero. x=v1t1⇒t1=xv1 x=v2t2⇒t2=xv2 Total displacement, x'=2x Total time, t=t1+t2 ∴ Average velocity, v=x't=2v1v2v1+v2 ⇒2v=1v1+1v2