Can anyone do question 11 on page 400 in active maths book 1? It is about integration, cannot do it at all... :(

leavingcert16
Raindrops grow as they fall, their surface area increases, and therefore the resistance to their falling increases. A raindrop has an initial downward velocity of 10 m s–1 and its downward acceleration is given by
a(t) = {9 – 0.9t if 0 ≤ t ≤ 10 0 for t > 10
The raindrop is initially 500 m above the ground.
(i) Find the velocity function v(t) of the raindrop after t seconds, 0 ≤ t ≤ 10.
(ii) Find v(10) and hence, write down the speed at which the raindrop hits the ground.
(iii) Find s(t), the distance travelled by the raindrop in t seconds, 0 ≤ t ≤ 10. (iv) How long does it take the raindrop to fall?

Lol Destroyer
yes

kinger
Integrate a(t) function to find v(t). Sub in 10 in v(t) function for part 2
Integrate v(t) function to find s(t) and go from there. Hope this helps.

Me
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