Question

A body moving with some initial velocity and having uniform acceleration attains a final velocity $vm/s$ after traveling x m. if its final velocity is $v=\sqrt{(}180-7x)$. find the acceleration of the body

• A. -3.5 m/s^2
• B. -8m/s^2
• C. -15 m/s^-2
• D. -30 m/s^2

Answer 1

The correct option is A -3.5 m/s^2

Given,

$v=\sqrt{180-7x}$. . . . . . . . . . . . . . .(1)

Acceleration, $a=\frac{dv}{dt}$

Differentiate equation (1) with respect to time $t$,

$a=-\frac{7}{2}(180-7x{)}^{-1/2}\frac{dx}{dt}$

$a=-3.5\frac{v}{\sqrt{180-7x}}$

$a=-3.5\frac{\sqrt{180-7x}}{\sqrt{180-7x}}$ (from equation 1)

$a=-3.5m/s^2$

The correct option is A.