How can you say that an object is moving in an accelerated motion?

if the time needed for the object to cross the same distance decreases by time.

For example:

1st second of motion, the object crosses exactly 1.0 meters of space.

2nd second of motion, the object crosses 3.0 meters of space.

Since the object has crossed more space (3.0m) in the 2nd second, than it did in the

first second(1.0m), we can conclude that the object is moving in an accelerated

motion.

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Another contributor added:

That answer is correct as far as it goes, but it's very important to be aware that

the discussion above only touches on one of several aspects of acceleration.

Somewhere in the past 100 years, somebody decided to name the skinny pedal

on the floor of the car the "accelerator". And ever since that day, everybody

thinks that "acceleration" means "speeding up". It doesn't.

"Acceleration" means: Changing speed (faster OR slower) OR changing direction.

The first answer said: "The time needed to cross the same distance decreases."

That's true. That's acceleration. That's what happens when you stomp the gas ...

you go faster. But that's not the only possible description of acceleration.

When you stomp the brake, you go slower. "The time needed to cross the same

distance increases." According to the strict definition, that's also 'acceleration'.

And what if you're driving along on cruise-control, your speed isn't changing at all,

but you're going around a gentle curve. Hold onto your seat belt, because that's

'acceleration' too. Acceleration doesn't always change your speed. If your direction

is changing, that's 'acceleration' too.