The mass is moving by uniformly accelerated motion, with initial velocity [tex]v_i=7.50 m/s[/tex] and acceleration [tex]a=0.55 m/s^2[/tex]. Its position at time t is given by the following law:
[tex]x(t)=v_i t + \frac{1}{2}at^2 [/tex]
where we take the initial position [tex]x_i=0[/tex] since we are only interested in the distance traveled by the mass.
If we put [tex]x(t)=d=3.5 km=3500 m[/tex] into the equation, the corresponding time t is the time it takes for the mass to travel this distance:
[tex] \frac{1}{2}at^2+v_it-d=0 [/tex]
[tex]4.9t^2+7.5t-3500 =0 [/tex]
And the two solutions for the equation are:
[tex]t=-25.5 s[/tex] --> negative, we can discard it
[tex]t=24.0 s[/tex] --> this is the solution to our problem
