Question

If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) ______ 

Options

• f²

• f³

• -f³

• -f²

Answer 1

If `t = v^2/3`, then `(-v/2 (df)/dt)` is equal to, (where f is acceleration) f². 

Explanation:

`t = v^3/3 ⇒ v^3 = 3t`

Differentiating both sides w.r.t.t., we get

`3v^2 (dv)/dt = 3`

⇒ `(dv)/dt = 1/v^2 = f`

⇒ `(df)/dt = -2/v^3. (dv)/dt = -2/v^3 xx 1/v^2`

⇒ `(-v/2 (df)/dt) = 1/v^4 = f^2`