Force applied to block moving along table

[uph0]

Homework Statement

An object of mass 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.

If friction force is ignored what will be the object's velocity in the direction when it reaches point A (point A is right of x = 0)

Homework Equations

conservation of energy
kinetic energy1 + potential erngery1 = kinetic energy2 + potential energy 2

textbook answer: c1/2m * (6mA/c1)^2/3

The Attempt at a Solution

using above formula
0 + 0 = 1/2mv² - c1t²/2

c1t = ma
t = ma/c1 (plug into above equation)

v = (ma²/c1)^1/2

 

[haruspex]

Inserting 'a' doesn't get you far because it is another variable that does not appear in the required answer. Instead of replacing t with a, you need to replace it with A. Can you get an equation relating t to A? (Might need some calculus - is that OK?)