Question

graph of 1/v versus x for a particle is shown. find time taken by particle to move from x=4 m to x=12 m​

Answer 1

Answer:

Time taken is 6 seconds.

Explanation:

To calculate the time using speed and distance, following formula is used:

$\text{Time =} \dfrac{\text{Distance}}{\text{Speed}}$

If t is the time taken,

d is the distance traveled and

v is the speed

The above formula can be represented as:

$t = \dfrac{d}{v}\\\Rightarrow t = \dfrac{1}{v} \times d ...... (1)$

We are provided with a graph between $\frac{1}{v}\text{ in } (m/s)^ {-1}$ and distance in metres here.

Area under the graph will provide us time taken as per equation (1).

Please refer to the image attached, we have to find the area of $\traingle ABC$.

As per the question statement, we have to find time taken for distance 4 to 12 metres i.e. 8 metres.

And Height of triangle = $2 - \frac{1}{2} \Rightarrow 1.5\ (m/s)^ {-1}$

$\text{Area of a triangle = }\dfrac{1}{2} \times \text{Base} \times \text{Height}$

$\Rightarrow \dfrac{1}{2} \times 8 \times 1.5\\\Rightarrow 6\text{ seconds}$

Time taken is 6 seconds.