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  • A body moving in a straight line with  speed , acceleration (a) and displ

A body moving in a straight line with  speed \left(V_0\right), acceleration (a) and displacement (s) if the displacement equation is given by -

S=\frac{A}{2}+\frac{B}{2} t+C t^3+D t^4
then Acceleration is given in the form of -
 

Option: 1

c t+4 \Delta ^2


Option: 2

6 c t+12 \Delta t^2


Option: 3

6 c t+\Delta t^2


Option: 4

6ct+t^4


Answers (1)

best_answer

 Displacement (S)= \frac{A}{2}+\frac{B}{2} t+C t^3+\Delta t^4 \\


Velocity (v)=\frac{d s}{d t} =\frac{d}{d t}\left(\frac{A}{2}+\frac{B}{2} t+c t^3+\Delta t^4\right) \\


=\frac{B}{2}+3 c t^2+4 D t^3

  Now,
   \text{accleration}(a) =\frac{d^2 s}{d t^2} \text { or } \frac{d v}{d t} \\


=\frac{d}{d t}\left[\frac{B}{2}+3 c t^2+4 \Delta t^3\right] \\


=0+6 c t+12 \Delta t^2 \\


=6 c t+12 D t^2

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