How is integrating F=ma from a=0 to a=20ms^2 wrong?

[gloomy owl]

.

[gloomy owl]

I integrated acceleration based on the graph from the acceleration at 0 meters to the acceleration at 8 meters to get 80 units of something. i'm not sure those units are still m/s^2 to be honest, but I didn't know what else they could be.
Then I did F=ma using 80 as the result of my integrated acceleration, and mass = 10 kg, so F= 10kg * 80 m/s^2

Finally I integrated the force from 0 meters to 8 meters, which... seems wrong thinking about it, because the force is already from 0 to 8 meters, but more importantly, 6400J is super wrong

I think W = the integral of F times dl is still right, where dl is the distance traveled

but maybe my w = integral of f=ma is wrong

thinking about it, we could have a graph of f=ma which takes a=2.5x and m=10kg, so f=25x, then w= integral of f

$w=\int ma$

[waxen lynx]

tazinator

[gloomy owl]

$w = \int_{0}^{8} madx $

$w = \int_{0}^{8} 10kg 2.5x dx$

[waxen lynx]

tazinator

[gloomy owl]

$w = 25 \int_{0}^{8} x dx$

[waxen lynx]

tazinator

[gloomy owl]

$w = \frac{25}{2} \big[x^2 \big]_{0}^{8}$

[waxen lynx]

tazinator

[gloomy owl]

i figured it out.

.close