Question

Find the standard equation of a body moving with a constant acceleration a along a coordinate line. The following properties are known. See attachment.

Answer 1

Hi that a lot of heavy signs to say that u start at the point s=0 with the velocity V
and a constant acceleration a.
now u want to find s at any time.
U can do that by intgrating a twice.
(as shown a is the second derevative of s)
so
\[\int\limits_{0}^{t} a dt = at +v _{0}\]
and
\[\int\limits_{0}^{t} (v+v _{0} )dt = 1/2at^2+v _{0}t+s _{0}\]

Answer 2

correction
\[\int\limits_{0}^{t}(at+v _{0})dt=1/2at2+v _{0} t+s _{0}\]