Question

The $x$-$t$ plot shown in the figure below describes the motion of the particle along $x$-axis, between two positions A and B. The particle passes through two intermediate points $P_1$ and $P_2$ as shown in the figure

• A. The instantaneous velocity is positive at $P_1$ and negative at $P_2$
• B. The instantaneous velocity is negative at both $P_1$ and $P_2$
• C. The instantaneous velocity is negative at $P_1$ and positive at $P_2$
• D. The instantaneous velocity is positive at both $P_1$ and $P_2$
• E. The instantaneous velocity is always positive

Hint:

Slope of $x$-$t$ graph gives velocity: upward slope $\Rightarrow$ positive, downward slope $\Rightarrow$ negative.

Answer 1

The Correct Option is A

Concept:
Velocity is the slope of the $x$-$t$ graph: \[ v = \frac{dx}{dt} \]

Step 1: Analyze slope at $P_1$.
At $P_1$, the graph is increasing with time $\Rightarrow$ slope positive. \[ v_{P_1} > 0 \]

Step 2: Analyze slope at $P_2$.
At $P_2$, the graph is decreasing $\Rightarrow$ slope negative. \[ v_{P_2} < 0 \]

Step 3: Conclusion.
\[ \text{Velocity positive at } P_1 \text{ and negative at } P_2 \]