calculus integration problems

[modern shard]

these r confusing and i understand integration but i dont know how to approach these

[plush quarry]

position is integral of velocity

velocity is integral of acceleration

[lucid crater]

If I gave you a function for the position of a particle over time, how would you find the velocity?

[sinful crown]

for the first one, integrate v(t) to get position and differentiate it to get acceleration. you can figure out +c based on the initial value given

for the second, use the value of dP/dt and the growth from day 1 to day 0 to figure out k, and then use that value of k to find pop after 7 days

[modern shard]

so you can just plug in (1, 11) for the first for + C

[sinful crown]

yeah

good thinking

[modern shard]

ok hold up

[sinful crown]

gtg but if you have any further questions hopefully someone else can chip in 👍

[modern shard]

ty