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Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Rest and Motion Kinematics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Rest and Motion Kinematics

A person travelling along a straight line moves with a uniform...

A person travelling along a straight line moves with a uniform velocity

v_1

for a certain duration and with a uniform velocity

v_2

for the next equal duration. The average velocity

v

is given by

Options

A $v = \dfrac{v_1 + v_2}{2}$
B $\dfrac{1}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2}$
C $v = \sqrt{v_1 v_2}$
D $\dfrac{2}{v} = \dfrac{1}{v_1} + \dfrac{1}{v_2}$

Correct answer

A. $v = \dfrac{v_1 + v_2}{2}$

Step-by-step solution

Let the equal time intervals be

t

.

Distance travelled in the first interval is

d_1 = v_1 t

.

Distance travelled in the second interval is

d_2 = v_2 t

.

Total distance travelled is

d = d_1 + d_2 = v_1 t + v_2 t = (v_1 + v_2) t

.

Total time taken is

T = t + t = 2t

.

Average velocity

v = \dfrac{\text{Total distance}}{\text{Total time}} = \dfrac{(v_1 + v_2) t}{2t} = \dfrac{v_1 + v_2}{2}

.

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