Question

The graph below shows the velocity of a particle moving in a straight line.
The ratio of average speed and average velocity of the particle in the time interval from $t=0$ to $t=6$

Answer 1

$\begin{array}{c}avjspeed=\frac{totaldis\tan ce}{totaltime}\\ avjvelocity=\frac{totaldisplacement}{totaltime}\end{array}$

Displacement=Area under graph

Displacement fice $t=6s=10\times 3+\frac{1}{2}\times 10\times 5-\frac{1}{2}\times 5\times 1$

$=45/2+30=105/2$

Distance fice $t=6s=\left|10\times 3\right|+\left(\frac{1}{2}\times 10\times 5\right)+\left(-\frac{1}{2}\times 5\times 1\right)$

$=30+\frac{50}{2}+\frac{5}{2}=\frac{115}{2}$

Average speed=distance=$115=23$

average velocity=distance$=105=21$