Question

The only force acting on a 2.0 kg body as it moves along a positive x axis has an x component Fx = −6 x N, with x in meters. The velocity at x = 3.0 m is 8.0 m/s. (a) What is the velocity of the body at x = 4.0 m? (b) At what positive value of x will the body have a velocity of 5.0 m/s?

Answer 1

Answer:a-0

b-2 m

Explanation:

Given mass of the body is 2 kg

Force acting on the body =-6x N

Velocity at x=3m is 8m/s

Now acceleration of the body is -3x

a=-3x

$\frac{vdv}{dx}$=-3x

vdv=-3xdx

integrating both sides we get

$\int vdv=\int -3xdx$

$\frac{v^2}{2}$=$\frac{x^2}{2}$+c

Now at x=3m v=8m/s

substituting values

c=$\frac{37}{2}$

Thus $v^2=-3x^2+37$

Velocity will be zero after $x=\sqrt{\frac{37}{3}}$

thus velocity of the body is zero at x=4 m

$\left ( b\right )$

v=5m/s

25=-3x^2+37

x=2 m