Question

A 500 g object moving along the x-axis experiences a force given by the following equation: F=[10N - (2N/m)x]x, where x is measured in meters. The object’s velocity atx = 0 m is 24 m/s. What is the object’s velocity (in m/s) at x = 5 m?

Answer 1

first you find the equation for acceleration
mass m = 500g = 0.5 kg
F=[10N - (2N/m)x]x,
ma = [10N - (2N/m)x]x,
a = 20x - 4x^2

then you need to replace a as following.

then you need to substitute this with a in equation and solve the equation as following.

continue solving and you get the following result.

Answer 2

mass m = 500g = 0.5 kg
F=[10N - (2N/m)x]x,
ma = [10N - (2N/m)x]x,
a = 20x - 4x²

and u = 24 m/s , x = 5 m , v= ?

from 3 rd equation of motion

v² - u² = 2ax

v² = 24² +2x(20x-4x² )

v² = 576+(40x² - 8x³ )

where x = 5 m

v² = 576

v = 24 m/s

Answer 3

F=[10N - (2N/m)x]x = ma

Here m = 500g = 0.5 Kg

Therefore

20x - 2x^2 = dv/dt

Threfore

v = 20xt - 2x^2t + 24

Put x = 5,we get

V(at x = 5) = 100t - 50t + 24

V(at x = 5) = 50t + 24

Answer 4

F=[10N - (2N/m)x]x = ma

Here m = 500g = 0.5 Kg

Therefore

20x - 2x^2 = dv/dt

Threfore

v = 20xt - 2x^2t + 24

Put x = 5,we get

V(at x = 5) = 100t - 50t + 24