First slide

Graphical representation-Motion in 1 d

Question

The velocity of a particle in a straight line motion is given by $v = 10 - 10 t$ . The correct graphical representation of displacement -time graph of motion is ( s-displacement, t - time)

Moderate

A
B
C
D

Solution

Given velocity time relation is $v = 10 - 10 t$ .
The relation between displacement and velocity $v = \frac{d s}{d t}$
$\begin{array}{l} ∴ d s = v d t \Rightarrow \int d s = \int v d t \\ S = \int_{}^{} v d t \\ = \int_{}^{} (10 - 10 t) d t \\ S = 10 t - \frac{10 t^{2}}{2} + c \end{array}$
The relation between S-t is a parabola with decreasing slope.
So 4^th option matches given options.
Therefore, the correct answer is (D)

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