# Physics. Life Sciences Math Problem. Physics and Natural Sciences (Math Problem Sample)

Physics problem.

source..[First name Last name]

[Instructor’s Name]

[Course Number]

21 March 2020

Physics and Natural Sciences

1) The particle moves along the positive X-axis, hence its velocity varies as V=αx, where α is a positive constant. Assuming that at the moment t=0 the particle was located at the point х=0, please find:

* how does velocity and acceleration of the particle depend on time / (time dependence of velocity and acceleration of the particle);

v=dXdt=ax…………1

From equation 1, we have

dXx=adt……2

Integrating both sides of equation 2 to get the equation of position in terms of time (t), we get

dXx=adt….3

2x=at+C…4

When t=0, x=0 from the boundary conditions

Substituting in equation 4,

C=0

Hence

x=at2……5

Squaring both sides,

x=(at)24 m

Velocity in terms of t

v=dXdt=a2t2 m/s

Acceleration in terms of t

a=dVdt=ddta2t2=a22 ms-2

* The average velocity of the particle during the time it runs the first S meters along its path.

To run s=meters,

S=x=(at)24……i