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How instantaneous velocity can be found by graphical method ?
Solution
$(1)$ Graphical Method :
– Suppose the below given $x \rightarrow t$ graph is for non-uniform motion of the car and we want to obtain graphically the value of velocity at time $t=4 \mathrm{~s}$.
For this case, the variation of velocity with time is found to be as shown in figure.
Suppose, by keeping $t=4 \mathrm{~s}$ in mind, if we take different time intervals $\Delta t_{1}, \Delta t_{2}, \Delta t_{3}, \ldots$ then for these time intervals displacement will be $\mathrm{P}_{1} \mathrm{P}_{2}, \mathrm{Q}_{1} \mathrm{Q}_{2}, \mathrm{~T}_{1} \mathrm{~T}_{2}, \ldots$ and corresponding displacement are $\Delta x_{1}, \Delta x_{2}, \Delta x_{3}, \ldots$
Similar Questions
Let us cell a motion, $A$ when velocity is positive and increasing $A^{-1}$ when velocity is negative and increasing. $R$ when velocity is positive and decreasing and $R^{-1}$ when velocity is negative and decreasing. Now, match the following two columns for the given $s=t$ graph.
| Colum $I$ | Colum $II$ |
| $(A)$ $M$ | $(p)$ $A^{-1}$ |
| $(B)$ $N$ | $(q)$ $R^{-1}$ |
| $(C)$ $P$ | $(r)$ $A$ |
| $(D)$ $Q$ | $(s)$ $R$ |
