Question

A particle of mass m moves along the x axis under the influence of a force given by F(x)=(3+2x)i. It starts from rest from the position x=0. Find the magnitude of its acceleration and velocity at position x.

Answer 1

Answer:

From Newton's second law of motion, acceleration can be calculated as follows:

F = ma

$F(x) = (3+2x)i = m a\\a_x=\frac{3+2x}{m}$

Use the third equation of motion to find the velocity at position x

$2as=v^2-u^2\\v=\sqrt{2a_xx+u^2}\\v=\sqrt{2\times \frac{3+2x}{m}\times x+0}\\v=\sqrt{\frac{6x+4x^2}{m}$