A) \[-1m/{{\sec }^{2}}\]
B) \[\frac{5}{4}m/{{\sec }^{2}}\]
C) \[-\frac{1}{2}m/{{\sec }^{2}}\]
D) \[-\frac{5}{4}m/{{\sec }^{2}}\]
Correct Answer: B
Solution :
Given equation \[s=a{{t}^{2}}+bt+6\] ??(i) Differentiating w.r.t. time, we get Velocity (v)\[=2at+b\] ??(ii) After 4sec, \[v=0\]and distance \[s=16\,metres\] \[\therefore 0=2a\times 4+b\Rightarrow 8a+b=0\] ?..(iii) and \[16=16a+4b+6\]Þ \[16=16a+4(-8a)+6\] \[\therefore \]\[a=-\frac{5}{8}\] But retardation in its motion is, \[2a=\frac{-5}{4}m/{{\sec }^{2}}\] \[\therefore \]Retardation \[=\frac{5}{4}m/{{s}^{2}}\](Retardation itself means ?ve).
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