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# physics help!?

question is in pic

### 1 Answer

- 7 months agoFavorite Answer
v(t) = 200 m/s - 10 m/s^2 * t seconds

v(t) = 0

0 = 200 - 10t

0 = 20 - t

t = 20

It's going to take 20 seconds to stop, at a minimum

s(t) = int(v(t) * dt) = 200t - 5t^2 + C

s(0) = 0

s(t) = 200t - 5t^2

s(20) = 200 * 20 - 5 * 20^2 = 20^2 * (10 - 5) = 400 * 5 = 2000

It'll need to be 2000 meters long

You need to accelerate from 0 m/s to 82.1 m/s in a space of 2000 meters

a(t) = a

v(t) = int(a * dt) = at + C

v(0) = 0

v(t) = at

s(t) = (1/2) * a * t^2 + C

s(0) = 0

s(t) = (1/2) * a * t^2

v(k) = 82.1

s(k) = 2000

82.1 = a * k

2000 = (1/2) * a * k^2

4000 = a * k^2

4000 / 82.1 = (a * k^2) / (a * k)

40000 / 821 = k

82.1 = a * k

82.1 = 40000a / 821

82.1 * 821 / 40000 = a

821 * 821 / 400000 = a

a = 1.6851025

You need a minimum acceleration of 1.69 m/s^2

48.7 seconds will elapse

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