Question

The speed-time graph of a particle moving along a fixed direction is shown in the figure. The distance traversed by the particle between $t=2s$ to $t=6s$ is

• A. $26m$
• B. $36m$
• C. $46m$
• D. $56m$

Answer 1

Answer: (B)

$36m$

Here,

From $t=0$ to $t=5$

The equation of the line gives the velocity of the particle at each instant.

$y=mx+c$

The slope of the line is obtained as:

$m=\frac{12-0}{5-0}=\frac{12}{5}$

and y-intercept of the line is zero. So, $c=0$.

Therefore, the line can be written as:

$v=\frac{12}{5}t$

Similarly, after $t=5$,

The slope of the line is obtained as:

$m=\frac{0-12}{10-5}=-\frac{12}{5}$

and y-intercept of the line is $c=24$.

$v=24-\frac{12}{5}t$

$s={\int }_2^5\left(2.4t\right).dt+{\int }_5^6(24-2.4t).dt$

$s=1.2(5^2-2^2)+(24\times 6-1.2\times 6^2)-(24\times 5-1.2\times 5^2)$

$21\times 1.2+24-1.2\times 36+1.2\times 25$

$25.2+24-43.2+30=36m$

Option $\text{B}$ is the correct answer