A) a constant
B) \[\propto {{s}^{3}}\]
C) \[\propto \frac{1}{{{s}^{3}}}\]
D) \[\propto {{s}^{5}}\]
E) \[\propto \frac{1}{{{s}^{5}}}\]
Correct Answer: D
Solution :
\[\because \]\[{{s}^{3}}\propto v\] \[\Rightarrow \] \[\frac{dS}{dt}=k{{s}^{3}}\] ?.. (i) \[\Rightarrow \] \[\frac{{{d}^{2}}s}{d{{t}^{2}}}=3k{{s}^{2}}\frac{ds}{dt}\] \[\Rightarrow \] \[\frac{{{d}^{2}}s}{d{{t}^{2}}}=3k{{s}^{2}}(k{{s}^{3}})\] [using Eq. (i)] \[\Rightarrow \] \[\frac{{{d}^{2}}s}{d{{t}^{2}}}=3{{k}^{2}}{{s}^{5}}\] \[\therefore \]From above it is clear that acceleration of a particle is proportional to 55.
You need to login to perform this action.
You will be redirected in
3 sec
