An object of mass m is placed at rest at the point x=0 on a horizontal table and

Question

An object of mass m is placed at rest at the point x=0 on a horizontal table and, at time t=0, a horizontal force is applied to it given by Fx=c1t where c1 is a known positive constant. The coefficient of friction between the table and the object is u.
a) If the friction force is ignored what will be the object's velocity in the x direction when it reaches the point x=A?
b) If the friction force is not ignored find the object's veloicty in the x direction as a function of time.

(I need detail explanation)

Explanation / Answer

accelarartion=c1t/m
velocity=c1t^2/m
x=.5*a*t*t
2A=.c1t^3/m
t=(2Am/c1)1/3

velocity=at=c1t^2/m=c1*(2A/c1)2/3

accelaration if friction not ignored=c1t-ugm/m

dv/dt=a

v=integtal(c1t-umg/m)

v=c1t2/2m -ugt

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