# Homework Help: Acceleration, velocity, displacement & time

1. Aug 26, 2014

### Baartzy89

1. The problem statement, all variables and given/known data
a = 2/(0.1v+1)
At t = 0; s = 0, v = 0

1) Derive a relationship between t and v
2) Derive a relationship between displacement (s) and v
3) Draw v vs t for 0s ≤ t ≤ 75s & s vs t for 0s ≤ t ≤ 50s graphs

2. Relevant equations
a = dv / dt
v = ds / dt

3. The attempt at a solution
For part (1) find the integral of dv = a.dt

For part (2) find the integral of ds = v.dt

For part (3) graph the equations found from the integrations above and graph a suitable scale.

Where I'm stuck;
1) Not really sure I've got the terms the correct way in part 2.
2) when integrating dt, what happens to this term? Does it become 0, 1 or t?

(I'm not looking for the answer, but to check my approach and also find out what happens to the dt term as this is the first course I've seen dt / d? terms rearranged.)

Thanks

2. Aug 26, 2014

### Staff: Mentor

Show us how you solved part 1, and what your result was. Have you had differential equations yet?

Chet

3. Aug 26, 2014

### SteamKing

Staff Emeritus
What usually happens when you integrate d(something)?

∫dx = ?

∫dt = ?

Isn't dt the same as 1$\cdot$dt?

You should take a quick integration review.