A truck is moving on a straight road with uniform acceleration. The following table gives the speed of the truck at various instants of time.
Speed $\left(m s^{-1}\right)$
$5$
$10$
$15$
$20$
$25$
$30$
Time $(s)$
$0$
$10$
$20$
$30$
$40$
$50$
Draw the speed-time graph by choosing a convenient scale. Determine from it
$(i)$ the acceleration of truck
$(ii)$ the distance travelled by the truck in $50$ seconds.
A truck is moving on a straight road with uniform acceleration. The following table gives the speed of the truck at various instants of time.
| Speed $\left(m s^{-1}\right)$ | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
| Time $(s)$ | $0$ | $10$ | $20$ | $30$ | $40$ | $50$ |
Draw the speed-time graph by choosing a convenient scale. Determine from it
$(i)$ the acceleration of truck
$(ii)$ the distance travelled by the truck in $50$ seconds.
The graph is as shown
$(i)$ Acceleration can be obtained by finding the slope of graph $AB$
Slope $=\frac{B C}{A C}=\frac{30-5}{50-0}=0.5 m s ^{-2}$
$(ii)$ Distance travelled by truck $=$ Area of trapezium $OABD$
$=1 / 2 \times$ sum of parallel sides $\times$ perpendicular distance
$=1 / 2 \times( AO + BD ) \times OD$
$=1 / 2 \times(5+30) \times 50=875 m$
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Time $(s)$
$0$
$10$
$20$
$30$
$40$
$50$
Speed $\left(m s^{-1}\right)$
$5$
$10$
$15$
$20$
$25$
$30$
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| Time $(s)$ | $0$ | $10$ | $20$ | $30$ | $40$ | $50$ |
| Speed $\left(m s^{-1}\right)$ | $5$ | $10$ | $15$ | $20$ | $25$ | $30$ |
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