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TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > M1 Maths

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Here are some basic notes on the content needed for M1 A Level maths exams.

Contents 1 SUVAT 2 Types of forces 3 Graphs 4 Comments

SUVAT

SUVAT equations are only used when acceleration is constant

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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
• position = displacement from a fixed origin
• velocity = rate of change of position (its magnitude is speed)
• acceleration = rate of change of velocity (as in above equation)
• distance = how much ground an object has covered during its motion
• speed = magnitude of velocity

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

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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.