TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > M1 Maths
Here are some basic notes on the content needed for M1 A Level maths exams.
SUVAT
SUVAT equations are only used when acceleration is constant
- s = height, distance, displacement
- u = initial velocity
- v = final velocity
- a = acceleration
- t = time
Acceleration (ms-2)
Velocity (ms-1)
- displacement = how far out of place something is from any position (vector quantity)
- position = displacement from a fixed origin
- velocity = rate of change of position (vector quantity; its magnitude is speed)
- acceleration = rate of change of velocity (vector quantity; as in above equation)
- distance = how much ground an object has covered during its motion (scalar quantity)
- speed = magnitude of velocity (scalar quantity)
Types of forces
- weight (w)
- friction (f)
- push and pull (p)
- normal reaction (r)
- tension (t) such as in a string, springs, rods
- thrust (s) such thrust in a spring or rod, but in opposite direction
Force = mass x acceleration
Weight = mass x gravitational pull
Tension is the same on both sides of a pulley
Rope in tension, not thrust
Newton's First Law - A resultant force is required to produce an acceleration
Calculating tension
A few equations of motion of a car
- D = driving force,
- T = tension,
- R = normal reaction or resistance
If a body is moving at a constant speed, the forces are in equilibrium
If a question includes air resistance, the equation for motion is
If the air resistance is proportional to the area perpendicular to motion, air resistance is kA
When combining forces, you are finding the resultant force
- A rough surface causes friction
- Smooth surface causes no friction
Forces on a car for example will be reduced by
- driving force (forwards)
- braking force (backwards)
- resistance (to motion) air or water act in opposite direction to velocity
Graphs
- Position - Time
- Gradient = Velocity
- Area = Nothing
- Velocity - Time
- Gradient = Acceleration
- Area = Displacement
- Distance - Time
- Gradient = Speed
- Area = Nothing
- Speed - Time
- Gradient = Magnitude of acceleration
- Area = Distance
(DISTANCE is NOT negative, ONLY POSITIVE)
Velocity at an instant can be found by drawing a tangent at the curve of the point
If you have a position, differentiate once for the velocity and differentiate twice for acceleration
Comments
Originally written by ixnayonthehombre on TSR Forums.
