Question

The position-time ($x$-$t$) graphs for two children $A$ and $B$ returning from their school $O$ to their homes $P$ and $Q$ respectively are as shown in the figure. Choose the incorrect statement regarding these graphs.

• A. $A$ lives closer to the school than $B$
• B. $A$ starts from the school earlier than $B$
• C. $A$ walks faster than $B$
• D. $A$ and $B$ reach home at the same time

Answer 1

Answer: (C)

(a) As $OP < OQ$, A lives closer to the school than $B$.

(b) For $x = 0$, $t = 0$ for $A$; while $t$ has some finite value for $B$. Therefore,
$A$ starts from the school earlier than $B$.
(c) Slope of $x$-$t$ graph is equal to the speed. Since the slope of $x$-$t$ for $B$ is greater than that for $A$. Therefore, $B$ walks faster than $A$.
(d) Corresponding to points $P$ and $Q$ the value of $t$ from $x$-$t$ graphs for $A$ and $B$ is same. Thus, both $A$ and $B$ reach home at the same time.