Please help me with any of these questions Im very stuck

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)

B) Analogously, the function p(t) describes the position or displacement describes of an object above ground level at time t. It is related ti the velocity via the equation v(t)= p'(t). Suppose an object has an initial displacement of p(0)=15 (in m). Solve the initial vale to determine an expression for p(t)

c) A Football (of the spherical variety is kicked upwards with initial velocity 10m/s from a platform 15m above the ground. Use your result from the pervious parts to find the time it takes for the football to hit the ground again.

Answer 1

A) v(t) = ∫gdt = gt + C

v(0) = 10 = 0 + C --> C = 10

v(t) = gt + 10 = -10t+10

B) p(t) = ∫v(t)dt = ∫gt+10dt = gt²/2 + 10t + C

p(0) = 15 = 0+0+C --> C = 15

p(t) = -5t²+10t+15

C)Find t when p(t) = 0

-5t²+10t+15 = 0

Divide through by -5

t²-2t-3 = 0

(t-3)(t+1) = 0

t = 3, -1 Choose the positive value

Time, t = 3 seconds