A) \[\frac{2}{3}m{{s}^{-2}}\]
B) \[-\frac{2}{3}m{{s}^{-2}}\]
C) \[\frac{20}{3}m{{s}^{-2}}\]
D) \[-\frac{20}{3}m{{s}^{-2}}\]
Correct Answer: D
Solution :
| [d] Slope of line \[=-\frac{2}{3}\] | |
| Equation of line is \[(V-20)=-\frac{2}{3}(S-0)\] | |
| \[\Rightarrow \] \[v=20-\frac{2}{3}S\] | ...(i) |
| Velocity at S =15 m, |
| i.e., \[v={{\left. \frac{dS}{dt} \right|}_{S=15m}}=20-\frac{2}{3}(15)=10\,m{{s}^{-1}}\] |
| Differentiating Eq. (i) w.r.t. time, |
| Acceleration \[=\frac{dv}{dt}=-\frac{2}{3}\frac{ds}{dt}\] |
| \[\therefore \] \[{{\left. \frac{dv}{dt} \right|}_{S=15m}}=-\frac{2}{3}{{\left. \frac{dS}{dt} \right|}_{S=15m}}=-\frac{20}{3}\text{m}{{\text{s}}^{-2}}\] |
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