Question

The velocity displacement graph of a particle moving along a straight line is shown in figure.

The velocity as function of ($0 \le x \le 1$) is

• A. -10 x
• B. -10 x+10
• C. 10 x-10
• D. -10 $x^2$+10x+10

Answer 1

Answer: (B)

-10 x+10

Answer 2

The problem asks us to find the velocity ($V$) as a function of displacement ($x$) from the given $V$-$x$ graph for a particle moving along a straight line.

The graph shows a straight line, which can be represented by the linear equation $V = mx + c$, where $m$ is the slope and $c$ is the $V$-intercept.

From the graph, we can identify two points:

1. At $x = 0$, $V = 10 \text{ ms}^{-1}$. This is the $V$-intercept, so $c = 10$.
2. At $x = 1 \text{ m}$, $V = 0 \text{ ms}^{-1}$.

Now, we calculate the slope ($m$) using these two points: $m = \frac{\text{change in }V}{\text{change in }x} = \frac{V_2 - V_1}{x_2 - x_1}$

Let $(x_1, V_1) = (0, 10)$ and $(x_2, V_2) = (1, 0)$. $m = \frac{0 - 10}{1 - 0} = \frac{-10}{1} = -10 \text{ s}^{-1}$

Substitute the slope ($m = -10$) and the $V$-intercept ($c = 10$) into the equation $V = mx + c$: $V = -10x + 10$

This equation describes the velocity as a function of displacement for $0 \le x \le 1$.