Determining the value of a constant

[Calpalned]

Example 3 shows the derivation of one of the kinematics equations. I am quite familiar with it. At the part where it says dx/dt = gt + constant, how does one determine if constant = x_0 or v_0? Thank you.

 

[Simon Bridge]

You use the physical description of the situation ... in this case, just checking the units are consistent should work.

 

[Calpalned]

You use the physical description of the situation ... in this case, just checking the units are consistent should work.

That makes sense. Thanks!

 

[Simon Bridge]

Since the constant term does not depend on time - you can always find the expression for it by putting $t=0$ into the equation.
In your example $v=gt+c$ you get $v(0)=c$ ... because you understand from the physics, that the time derivative of displacement is velocity.