about English expressions

speed up
Accelerate, expedite, increase the rate, as in The car speeded up as it went downhill, or It's difficult to speed up production without new equipment.

hurry up
Carried out as rapidly as possible, especially in the final minutes of a football game: a hurry-up offense.

get going
Get something going. Start something, get something into full swing. For example, Let's get going.

make tracks
Move or leave in a hurry, as in If we're going to catch the first show, we'd better make tracks.

get cracking
Hurry up; also, start working. For example, Let's get cracking.

step on it
Hurry up, go faster, as in you can tell the taxi driver to Step on it or we are going to be late.

get a move on
Hurry up; also, start working. For example, Get a move on, it's late

They are actually very similar.

Speed up and hurry up - have the meaning of asking people to do faster, go faster, start quickly.
The rest - have the meaning of let's start now.

Speed up and hurry up are more formal ways (in the informal ways) which sometimes, you may use in writing. However, the rest definitelly will only be seen in dialogues or conversations.

Some more examples:

Let's get back on track.
Let's crack on.
Move.