Gujarati
Hindi
7. MOTION
hard

Draw a velocity versus time graph for a body which starts to move with velocity $'u^{\prime}$ under a constant acceleration $'a'$ for time $t$. Using this graph derive an expression for distance covered $'S'$ in time $'t^{\prime}$

Option A
Option B
Option C
Option D

Solution

The graph is as shown

The area under the graph is the area of the rectangle $OACD$ plus the area of the triangle ABC on top of it as shown in figure. The rectangle has a height $u$ and a length $t$. This area is the distance travelled by the object.

Hence, $S=u t+\frac{1}{2} \times t \times(v-u)$ $….(1)$

But from the expression $v=u+a t,$ we have

at $=v-u$. Substituting in equation $(1),$ we have

$S=u t+\frac{1}{2}(a t) t=u t+\frac{1}{2} a t^{2}$

Standard 9
Science

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