acceleration
or d2x/dt2, the rate of change of the velocity with respect to t. If the velocity is positive (that is, if the particle is moving in the positive direction), the acceleration is positive when the particle is speeding up and negative when it is slowing down. However, if the velocity is negative, a positive acceleration means that the particle is slowing down and a negative acceleration means that it is speeding up.
In the preceding paragraph, a common convention has been followed, in which the unit vector i in the positive direction along the line has been suppressed. Acceleration is in fact a vector quantity, and in the 1-dimensional case above it is equal to 
.
When the motion is in two or three dimensions, vectors are used explicitly. The acceleration a of a particle is a vector equal to the rate of change of the velocity v with respect to t. Thus a=dv/dt. If the particle has position vector r, then 
. When Cartesian coordinates are used, r = xi + yj + zk, and then 
.
If a particle is travelling in a circle with constant speed, it still has an acceleration because of the changing direction of the velocity. This acceleration is towards the centre of the circle and has magnitude 
where v is the speed of the particle and r is the radius of the circle.
Acceleration has the dimensions LT−2, and the SI unit of measurement is the metre per second per second, abbreviated to ms−2.
- modus ponens
- modus tollens
- moment
- moment
- moment estimator
- moment generating function
- moment of inertia
- moment of momentum
- momentum
- Monge, Gaspard
- Monge point
- monic polynomial
- monoid
- monomorphism
- monotone convergence theorem
- monotonic function
- monotonic sequence
- Monte Carlo methods
- Monty Hall problem
- Moore-Penrose inverse
- Mordell Conjecture
- Morera's Theorem
- Morley's Theorem
- morphism
- Morse Theory