EXPEDITION /ˌek.spəˈdɪʃ.ən/ (n):

# Speed in doing something.

We will deal with your order with the greatest possible expedition.

EXPEDITIOUS /ˌekspəˈdɪʃəs/ (adj):

# That works well without wasting time, money, etc.

The most expeditious method of dealing with the situation.

EXPEDITIOUSLY /ˌekspəˈdɪʃəsli/ (adv):

# In a way that works well without wasting time, money, etc.

The work was carried out as expeditiously as possible.

SPEED /spiːd/ (v): 

# [transitive] speed something (formal) to make something happen more quickly.

The drugs will speed her recovery.

More is needed to speed the development of a safe and effective vaccine.

SPEED UP (phrasal verb):

# ​To move or happen faster; to make something move or happen faster.

The train soon speeded up.

Can you try and speed things up a bit?

They have speeded up production of the new car.

The daring new technique dramatically speeded up the construction process.

ACCELERATE /əkˈseləreɪt/ (v):

# [intransitive, transitive] to happen faster or earlier; to make something happen faster or earlier.

Inflation continues to accelerate.

Accelerate something: Exposure to the sun can accelerate the ageing process.

ACCELERATION /əkˌseləˈreɪʃn/ (n):

# [uncountable, singular] acceleration (in something): an increase in how fast something happens.

An acceleration in the rate of economic growth.