Question

The velocity-time graph of a body moving along a straight line is given below find:
(a) Average velocity in whole time of motion
(b) Average speed in whole time of motion
(c) Draw acceleration vs time graph.

Answer 1

a. Area of graph above time axis
$A=\frac{1}{2}\times (8-4)\times 10=60m$
Area of graph below time axis
$B=\frac{1}{2}\times 4\times 10=20m$
Average velocity in whole time of motion
$\overrightarrow{v}=\frac{Displacement}{Totaltime}$ = $\frac{AreaA-AreaB}{Totaltime}$
= $\frac{60-20}{12}=3.33m{s}^{-1}$
b. Average speed in whole time of motion
$v_{av}=\frac{Totaldistance}{Totaltime}=\frac{AreaA+AreaB}{Totaltime}=\frac{60+20}{12}=6.67m{s}^{-1}$
c. Acceleration:
From 0 to 2 s;
$a=\frac{v_2-v_1}{t_2-t_1}=\frac{10-0}{2-0}=5m{s}^{-2}$
From 2 to 6 s :
$a=\frac{v_2-v_1}{t_2-t_1}=\frac{10-10}{6-2}=0$
From 10 to 12 s: $a=\frac{v_2-v_1}{t_2-t_1}=\frac{-10-10}{10-6}=-5m{s}^{-2}$
From 10 to 12 s:
$a=\frac{v_2-v_1}{t_2-t_1}=\frac{0-(-10)}{12-10}=5m{s}^{-2}$
Acceleration vs time graph is drawn in figure.