The acceleration of the particle
A) is constant
B) increases linearly with x
C) increases parabolically with x
D) none of these
Correct Answer: B
Solution :
[b] From the graph, velocity-displacement equation can be written as: \[v={{v}_{0}}+\alpha x\] ??(1) Here \[{{v}_{0}}\] and \[\alpha \] are positive constants. Differentiating (1) with respect to x we get \[\frac{dv}{dx}=\alpha =\] constant Acceleration of the particle can be written as \[a=v.\frac{dv}{dx}=({{v}_{0}}+\alpha x).\alpha \] \[\alpha -x\]equation is a linear equation. Thus acceleration increases linearly with x.
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