Dear student,Given,Velocity, v=180-16x12we have,v=dxdt (1)x→displacementAcceleration is,a=dvdt⇒a=dvdx×dxdt=dvdx×v (2) (Using equation 1)v=180-16x12⇒v2=180-16xDifferentiating with respect to x,2v×dvdx=0-16⇒v×dvdx=-8⇒a=-8m/s2, Option 3 (Using equation 2)Regards

180-16x m/a then

D e a r s t u d e n t, G i v e n, V e l o c i t y, v = {(180 - 16 x)}^{\frac{1}{2}} w e h a v e, v = \frac{d x}{d t} . . . . . . . . . (1) x \to d i s p l a c e m e n t A c c e l e r a t i o n i s, a = \frac{d v}{d t} \Rightarrow a = \frac{d v}{d x} \times \frac{d x}{d t} = \frac{d v}{d x} \times v . . . . . . . . . . . . . . . (2) (U \sin g e q u a t i o n 1) v = {(180 - 16 x)}^{\frac{1}{2}} \Rightarrow v^{2} = 180 - 16 x D i f f e r e n t i a t i n g w i t h r e s p e c t t o x, 2 v \times \frac{d v}{d x} = 0 - 16 \Rightarrow v \times \frac{d v}{d x} = - 8 \Rightarrow a = - 8 m / s^{2}, O p t i o n 3 (U \sin g e q u a t i o n 2) R e g a r d s .

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