Given below are the velocity-time graph of five particles, A, B, C, D and E. The correct graph from the following v-t plot in which the velocity if the particle is a function of t2 is
The Correct Option is A
Approach Solution - 1
In a graph where the velocity is a function of \( t^2 \), the graph should show a curve that increases non-linearly with time, indicating that the rate of change of velocity increases over time. In this case, the graph labeled A shows the characteristic curve of a velocity-time plot where the velocity is increasing with time in such a way that it is related to \( t^2 \). The relationship is quadratic, which fits the description of a function of \( t^2 \). Thus, graph A is the correct one for this scenario
The correct option is (A) :
Approach Solution -2
If the velocity of a particle is a function of time squared, i.e.,
$v = k t^2$ (where $k$ is a constant),
then the velocity-time graph will be a parabola opening upwards if $k > 0$.
Among the given graphs, the one that curves upwards in a parabolic shape represents a velocity that increases with the square of time.
Therefore, the correct graph is the one showing a parabolic curve.
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