Please help me with this maths question

Question

Near the surface of the Earth, we estimate the acceleration due to gravity to be consistent to the value g=-10(in m/s^2).

A) velocity (v(t)) describes the speed and direction of an object at time t. It is related to gravity via the equation g= v'(t). suppose an object has an initial velocity of v(0)=10 (in m/s) solve the initial value problem to determine an expression for v(t)

Answer 1

dv(t)/dt = g

dv(t) = g dt

Integrate both sides. v(t) is integrated from v(0) to v(t) and t is integrated from 0 to t.

∫ dv(t) = ∫ g dt

v(t) - v(0) = gt

v(t) = gt + v(0)

Use the initial condition (v(0) = 10 m/s) such that

v(t) = gt + 10 m/s.