A) \[\frac{x}{y}=\frac{\beta }{\alpha }\]
B) \[\frac{\beta }{\alpha }=\frac{{{t}_{2}}y}{{{t}_{1}}x}\]
C) \[x=y\]
D) \[\frac{x}{y}=\frac{\beta {{t}_{1}}}{\alpha {{t}_{2}}}\]
Correct Answer: A
Solution :
[a] : Slope of v - t graph = Acceleration. \[\alpha =\frac{{{v}_{0}}}{{{t}_{1}}},\beta =\frac{{{v}_{0}}}{{{t}_{2}}}\] \[\therefore \]\[\frac{\beta }{\alpha }=\frac{{{t}_{1}}}{{{t}_{1}}}\] Displacement = Area under v - t graph \[\therefore \]\[x=\frac{1}{2}{{t}_{1}}\times {{v}_{0}}\]and\[y=\frac{1}{2}{{t}_{2}}\times {{v}_{0}}\] Hence, \[\frac{x}{y}=\frac{{{t}_{1}}}{{{t}_{2}}}=\frac{\beta }{\alpha }\]You need to login to perform this action.
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