**Forces and Motion**

- see also:

**Some basics:**

**average speed**= distance travelled / time elapsed**velocity**is a direction and speed vector**instantaneous velocity**is the gradient of a distance vs time graph of the object's motion**average acceleration**= change in velocity / time elapsed**instantaneous acceleration**is the gradient of a velocity vs time graph of the object's motion**relative velocity**between two objects is the vector subtraction of the two velocities (see also Einstein)**terminal velocity**is the vertical velocity of a falling object at which the force of air resistance is just sufficient to balance the gravitational force on its mass**acceleration of a free falling body**at sea level and 45deg latitude = 9.80 m/sec^{2}

**Newtonian laws of motion of objects:**

**three laws of motion:****the law of inertia:**- a body remains at rest or continues to move with constant velocity unless acted upon by a net force

**the law of force and acceleration:**- a force is needed to change the velocity of an object, that is to
accelerate it. When a net force Fn does act on an object, it
produces an acceleration a in the direction of the force, given by:
**net force = mass of object x acceleration**- force in newton, mass in kg, acceleration in m/sec
^{2} - nb. force is the area under a acceleration vs time curve

- force in newton, mass in kg, acceleration in m/sec
- at any given instant, the instantaneous net force produces an instantaneous acceleration as above.

- a force is needed to change the velocity of an object, that is to
accelerate it. When a net force Fn does act on an object, it
produces an acceleration a in the direction of the force, given by:
**the law of reacting forces:**- to any force which acts on a body, there is always an equal and
opposite reaction force acting on another body thus
**momentum is conserved**in any collision process - ie. if there is no external force acting on a system of bodies,
the momentum of the system does not change
**momentum**= mass x velocity- eg. momentum of recoil of gun = - momentum of bullet
**impulse**= change in momentum = force x time elapsed

- to any force which acts on a body, there is always an equal and
opposite reaction force acting on another body thus

**the law of universal gravitation:**- every particle in the universe attracts every other particle with a
force that is directly proportional to the product of the masses of the
two particles & inversely proportional to the square of the distance
between the centres of mass
**force of gravity**= Gm_{1}m_{2}/s- G = gravitational constant = 6.67 x 10-11 newton-m2/kg2
- s = distance between centres of mass of two objects in metres
- m
_{1}m_{2}are the respective masses of each object in kg

- every particle in the universe attracts every other particle with a
force that is directly proportional to the product of the masses of the
two particles & inversely proportional to the square of the distance
between the centres of mass

**Einstein's theory of relativity:**

- sorry can't go faster than speed of light as you get heavier & need
exponentially more energy to go faster:
**mass = mass at rest / sqrt (1 - v**, where v = speed & c = speed of light^{2}/c^{2})

- relative velocity of two objects:
**relative velocity**, where v_{AB}= (va - vb) / sqrt (1 - v_{a}v_{b}/c^{2})_{a}, v_{b}= velocity of each object & c = speed of light