Question

An object is moving along a straight line as shown in the figure. It moves from $O$ to $P$ in $10s$ and returns from $P$ to $R$ in $20s$.

With reference to the above given figure, match the Column I (average velocity and average speed) with Column II (values) and select the correct answer from the codes given below.

Column I		Column II
A	The average velocity and the	1	$-0.5m{s}^{-1},3m{s}^{-1}$ average speed of the object in going from $O$ to $P$ are
B	The average velocity and the	2	$+2m{s}^{-1},2m{s}^{-1}$ average speed of the object in going from $O$ to $P$ and back to $R$ are
C	If the object moves from $O$ to $Q$ and back to $R$ in $40s$, then	3	$-\frac{2}{3}m{s}^{-1},2m{s}^{-1}$ the average velocity and average speed of the object are

• A. $A-(1),B-(3),C-(2)$
• B. $A-(1),B-(2),C-(3)$
• C. $A-(2),B-(1),C-(3)$
• D. $A-(2),B-(3),C-(1)$

Answer 1

Answer: (D)

A. Here, average velocity $=\frac{\text{ displacement }}{\text{ time interval }}$
$=\frac{x_2-x_1}{t_2-t_1}=\frac{+20-0}{10s}=+2m{s}^{-1}$
Average speed $=\frac{\text{ Total path length }}{\text{ Time interval }}$
$=\frac{OP}{t_2-t_1}=\frac{20m}{10s}=2m{s}^{-1}$
B. For path travelled from $O$ to $P$ and and back to $R$, Average velocity $=\frac{\text{ Displacement }}{\text{ Time interval }}=\frac{x_2-x_1}{t_2-t_1}$
$=\frac{(-20)-0}{(10+20)}=-\frac{20}{30}m{s}^{-1}$
$=-\frac{2}{3}m{s}^{-1}$
Average speed $=\frac{\text{ Path length }}{\text{ Time interval }}$
$=\frac{OP+PR}{10+20}$
$=\frac{(20+40)m}{30s}=\frac{60}{30}m{s}^{-1}$
$=2m{s}^{-1}$
C. When object moves from $O$ to $Q$ and back to $R$, then Average velocity $=\frac{x_2-x_1}{t_2-t_1}=\frac{[(-20)-0]m}{40s}$
$=-\frac{20}{40}m{s}^{-1}=-0.5m{s}^{-1}$
Average speed $=\frac{OQ+QR}{\Delta t}$
$=\frac{(50+70)m}{40s}=\frac{120}{40}m{s}^{-1}=3m{s}^{-1}$
Hence, $A\to 2,B\to 3$ and $C\to 1$.