Question

The velocity time graph of a particle along a straight line is given in figure. In the time interval $t=0$ to $t=8$ seconds, answer the following questions:
The value of $[\frac{magnitudeof\mathrm{maximum}velocity}{magnitudeofaveragevelocity}$ for the given interval is

• A. $\frac{8}{9}$
• B. $\frac{8}{3}$
• C. $\frac{16}{9}$
• D. $\frac{16}{3}$

Answer 1

The correct option is C $\frac{16}{9}$

From the graph we see that the maximum speed of the particle $v_{max}=4m/s$

And we know average speed $v_{avg}=\frac{\text{total distance covered}}{time}$-----(A)

Also the area under velocity verses time graph gives us the distance covered.

Total area under the graph above the axis$=2(\frac{1}{2}base\times altitude)+(length\times breadth)=12m$

Total area under the graph below the axis $=2(\frac{1}{2}base\times altitude)+length\times breadth=6m$

Total area under the graph=distance covered $=12+6=18$

Now putting the above value in A we get,

$v_{avg}=\frac{18}{8}m/s$

Now as asked in question

$\frac{\text{maximum speed}}{\text{average speed}}=\frac{4\times 8}{18}=\frac{16}{9}$