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JIPMER 2009

Exam: JIPMER
Year: 2009
Subject: Physics
Chapter: Motion in One Dimension

JIPMER 2009 · Physics · Motion in One Dimension

A car moves from X to Y with a uniform speed v_u and returns to Y...

A car moves from

X

to

Y

with a uniform speed

v_u

and returns to

Y

with a uniform speed

v_d

. The average speed for this round trip is

Options

A $\frac{2 v_d v_u}{v_d+v_u}$
B $\sqrt{v_u v_d}$
C $\frac{v_d v_u}{v_d+v_u}$
D $\frac{v_u+v_d}{2}$

Correct answer

A. $\frac{2 v_d v_u}{v_d+v_u}$

Step-by-step solution

Let

t_1 and

t_2

be times taken by the car to go from

X

to

Y

and then from

Y

to

X

respectively. Then,

t_1+t_2=\frac{X Y}{v_u}+\frac{X Y}{v_d}=X

Y\left(\frac{v_u+v_d}{v_u v_d}\right)

Total distance travelled

=X Y+X Y=2 X Y

Therefore, average speed of the car for this round trip is

\begin{aligned} v_{\mathrm{av}} & =\frac{2 X Y}{X Y\left(\frac{v_u+v_d}{v_u v_d}\right)} \\ \text{ or } \quad v_{\mathrm{av}} & =\frac{2 v_u v_d}{v_u+v_d}\end{aligned}

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