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The speed (v) and time (t) for an object...

The speed (v) and time (t) for an object moving along straight line are related as `t^(2)+100=2vt` where v is in meter/second and t is in second. Find the possible positive values of v.

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(i) `y=e^(-x)=e^(z)` where `z=-x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=(e^(z))(-1)=-e^(z)=-e^(-x)`
(ii) `y=4 sin 3x=4 sinz` where `z=3x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=4 (cos z)(3)=12 cos 3x`
(iii) `y=4e^(x^(2)-2x)=4e^(z)` where `z=x^(2)-2x " "` so `(dy)/(dx)=(dy)/(dz)xx(dz)/(dx)=4 (e^(z))(2x-2)=(8x-x)e^(x^(2)-2x)`
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