integrating a parametric equation

[gr3mlin]

how do u integrate a parametric equation? we're using the equation change in x =.5at^2+initial velocity * time plus initial height. initial velocity 25.6. gravity is -9.8m/s. change in x is 59 m/s. help me integrate please

 

[galactus]

how do u integrate a parametric equation? we're using the equation change in x =.5at^2+initial velocity * time plus initial height. initial velocity 25.6. gravity is -9.8m/s. change in x is 59 m/s. help me integrate please

It would appear you mean \(\displaystyle x=\frac{1}{2}a\cdot t^{2}+v_{0}t+h_{0}, \;\ v_{0}=25.6\)

\(\displaystyle \frac{1}{2}at^{2}+25.6t+h_{0}\)

This is the x coordinate of a particle moving with constant acceleration.

Why integrate a position equation?. The change in x would indicate differentiating.

Perhaps there is more to it?. Am I missing something?.

But, to integrate: \(\displaystyle \frac{1}{6}at^{3}+12.8t^{2}+h_{0}t\)

 

[gr3mlin]

my bad, I worded it wrong. u are righ with the equation. we want to derive the equation to get a velocity equation. from there we want to integrate to find the total distance the projectile traveled.

 

[galactus]

To find velocity, you differentiate the position equation.

This gives \(\displaystyle v(t)=\frac{dx}{dt}=at+25.6\)

Please post the problem exactly as given.