91Ó°ÊÓ

The graph crankshaft is drawn between angular velocity versus time.

The following graph shows the graph of angular velocity versus time for a crankshaft of car.

The angular acceleration of the crankshatt is,

$\begin{array}{l}\mathrm{Î\pm }=\frac{\left({\mathrm{Ó\neg }}_1−{\mathrm{Ó\neg }}_0\right)}{t_1−t_0}\\ \mathrm{Î\pm }=\frac{(150\text{rad}/\text{s}−50\text{rad}/\text{s})}{(1\text{s}−0\text{s})}\\ =100\text{rad}/{\text{s}}^2\end{array}$

Thus, the angular acceleration of the crankshaft at $t=1\text{s}$is $100\text{rad}/{\text{s}}^2$.

The angular acceleration of the crankshaft is,

$\begin{array}{l}x=\frac{\left({\mathrm{Ó\neg }}_3−{\mathrm{Ó\neg }}_2\right)}{t_3−t_2}\\ \mathrm{Î\pm }=\frac{(250\text{rad}/\text{s}−250\text{rad}/\text{s})}{(3\text{s}−2\text{s})}\\ =0\text{rad}/{\text{s}}^2\end{array}$

Thus, the angular acceleration of the crankshaft at $t=3\text{s}$is $0\text{rad}/{\text{s}}^2$.$\begin{array}{l}x=\frac{\left({\mathrm{Ó\neg }}_3−{\mathrm{Ó\neg }}_2\right)}{t_3−t_2}\\ \mathrm{Î\pm }=\frac{(250\text{rad}/\text{s}−250\text{rad}/\text{s})}{(3\text{s}−2\text{s})}\\ =0\text{rad}/{\text{s}}^2\end{array}$

The angular acceleration of the crankshaft is,

$\begin{array}{l}\mathrm{Î\pm }=\frac{\left({\mathrm{Ó\neg }}_5−{\mathrm{Ó\neg }}_4\right)}{t_5−t_4}\\ \mathrm{Î\pm }=\frac{(200\text{rad}/\text{s}−250\text{rad}/\text{s})}{(5\text{s}−4\text{s})}\\ =−50\text{rad}/{\text{s}}^2\end{array}$

Thus, the angular acceleration of the crankshaft at $t=5\text{s}$is $−50\text{rad}/{\text{s}}^2$.