Calculus Help

Question

an object is fired vertically upward with an initial velocity v(0) = v₀  from an initial position s(0)=s_{0. Answer part A and B below.}

 A. For v₀=39.2m/s and s₀=27m find the position and velocity function for all times at which the object is above the ground.

The velocity function is v(t)=_______________.

 

 

 

I am sorry I do not have question B yet, once I answer this I will get question B so I will leave it in comment.

Thanks for help in advance.

 

Answer 1

Force = ma = mg where g is the acceleration due to gravity near the Earth's surface.  g = -9.8 m/s².

 

v(t) = ∫g dt = g*t + v₀ = (-9.8 m/s²)*t + (39.2 m/s)

 

The object's height, h, is:

 

h(t) = ∫ v(t) dt = ∫(gt + v₀) dt =  (1/2)gt² + v₀t + s₀