Calculus related problem. Need someone to check my thought process.?

Question

Going over some past material for a final coming up. It's been a while so I want to see if I'm doing the steps correctly. 
"A person is holding a gun 2 meters above the ground and fires a bullet straight up. It takes 10 seconds for the bullet to reach its highest point, g = 9.8m/s^2"
a(t) = -9.8 
v(t) = integralOf (a(t)) = -9.8t + C
v(10) = 0 = -98 + C, C = 98 
s(t), the position, = integralOf(v(t)) 
= -4.9t^2 + 98t + 2

Alvin · Answer

Yes, you are right. 
However, if this was a  physics question . You would just know the Kinematic equations.   I always remember the position equation from 
physic and work backwards  with derivatives to determine the 
others. 
s(t) =  h_i + v_i*t + (1/2)at^2
ds(t)/dt = v(t)    
v(t) = v_i+at  
dv(t) /dt = a(t) 
a(t) =     a
Reference:
http://www.physicsclassroom.com/class/1DKin/Lesson-6/Kinematic-Equations-and-Free-Fall

? · Answer

you get height 492 m.
You have velocity = g t= 98.
height is related to the velocity by
h= v^2/(2g) =490, Total height = 490+2=492 m
Your answer is corect.

Lacne · Answer

I would use your kinematics equations. But if this is a calc class better do an integration over the function.  Looks right to me.

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Calculus related problem. Need someone to check my thought process.?

3 Answers