# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-calculus-kinematics.html


## Kinematics

"The factor most ignored in discussing interstellar flight is the kinetic energy that must be invested in the ship to make its tons of matter move at a substantial fraction of the speed of light" Barney Oliver


#### Kinematics


##### What you have to know:

- The derivatives of all known functions (If not, check this lesson)
- How to integrate (If not, check this lesson)
- You must be able to manipulate exponential expressions. (If not, check this lesson)
- You must be able to manipulate logarithmic expressions. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Check out this presentation .
- 3. Read these notes .

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359): 21C

##### Key Points

- You should be able to apply calculus to kinematics, linking displacement, velocity, acceleration and distance travelled. Velocity and acceleration are given by \( v = \frac{ds}{dt} \) and \( a = \frac{dv}{dt} = \frac{d^2s}{dt^2} \). The change in velocity from \( t = a \) to \( t = b \) is \[ \int_a^b a\,dt, \] the change in displacement from \( t = a \) to \( t = b \) is \[ \int_a^b v\,dt, \] and the distance travelled between \( t = a \) and \( t = b \) is \[ \int_a^b |v|\,dt. \]

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