# Mechanics 1

- Created by: S_F
- Created on: 19-05-22 09:22

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- Mechanics 1.0
- Position vectors
- x + s = new position vector
- x = original position vector
- s= displacement from x

- For particles travelling at constant velocity, s=vt
- s, u, a and v are all vectors while t is scalar. Vectors cannot be squared so V2 = u2 + (2as) cannot be used

- x + s = new position vector
- Constant acceleration formulae in two dimensions
- s = displacement in metres
- u = initial velocity in metres per second
- v = final velocity
- At the object's maximum height, the vertical velocity is momentarily zero before it starts falling again

- a = acceleration in metres per second squared
- if an object is moving freely under gravity, the acceleration is just g

- t = time
- Modelling assumption: the object is a particle - its dimensions can be ignored and air resistance does not act on it

- Calculus in kinematics using vectors
- If a particle is moving in a straight line with acceleration that varies with time, you need to use calculus
- To find an equation for velocity, differentiate the equation for displacement with respect to time
- To find an equation for a, differentiate the equation for velocity with respect to time
- s ------------- v ------------- a -------------differentiate down and Integrate in the opposite way

- If a particle is moving in a straight line with acceleration that varies with time, you need to use calculus
- Magnitude of a vector
- The direction of a velocity vector gives the direction of motion of the object and the direction of its acceleration vector is the direction of the resultant force
- speed is the magnitude of velocity - use Pythagoras' theorem
- s = hi + vj direction: tan-1(v/h)

- Projectile motion
- Split velocity of projection into two components
- A projectile with speed u at an angle to the horizontal has two components of initial velocity
- horizontal: parallel to the x-axis
- ucos(angle) - cosine cuts through the angle

- vertical: usin(angle)

- horizontal: parallel to the x-axis

- A projectile with speed u at an angle to the horizontal has two components of initial velocity
- Split motion into horizontal and vertical components too
- Deal with the vertical and horizontal components separately using the suvat equations.
- The only thing that is the same in both directions is time - so this connects them

- There is only vertical acceleration and due to gravity - horizontal acceleration is zero
- velocity = zero at maximum velocity

- Split velocity of projection into two components

- Position vectors

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