Differentiate escape velocity from acceleration?

Question

If you built a rocket with acceleration more than 9.8 m/s^2, it would eventually leave the earth, right? So where does the concept of escape velocity fit into this?

Answer 1

velocity is the rate of speed. acceleration is the rate of increasing speed

Answer 2

Escape velocity is determined by finding the amount of potential energy required to lift a body from the surface of the Earth to infinity.

Acceleration is what is needed to get to the escape velocity. If you were accelerated at just greater than 1 g for 10 seconds, how far would you get?

Answer 3

Escape velocity is the SPEED at which you could break free from Earth's gravitational field (..if you maintained that speed for a long time)

Acceleration is the RATE OF CHANGE in speed. For instance, it might take a rocket ship 10 minutes to go from 0 mph to escape velocity. Don't confuse this type of acceleration with the 9.8 m/s^2 you mentioned in your question--that's gravitational acceleration and doesn't necessarily involve actual movement.

Answer 4

Ok, it sounds like you're pretty physics-savvy, so I'll make this a bit technical. The thing to keep in mind here is that the acceleration due to Earth's gravity changes with distance from the center. It's only 9.8m/s^2 at the surface, which is roughly 6,000 km from the center. Since gravity falls off as the distance squared, 12,000 km from the center (6,000 km from the surface) the acceleration is only 1/4 of that, or 2.45 m/s^2, so you'd need less force to "fight" against gravity up there. Since the acceleration is changing, we need some calculus to the rescue.

Remember, acceleration is just force per unit mass. So, if we integrate that acceleration over the distance from the surface we'll get the energy per unit mass required to get out to some distance from the surface (since energy is just force x distance). In other words, as you get further and further from the Earth, gravity is even weaker and you need less and less energy to get further and further. The total amount of energy per unit mass adds up as you leave the surface, but it becomes asymptotic as your distance goes to infinity and converges on a single, finite number when you solve for the limit. Once you're "at infinity", the total energy per unit mass is all in the potential energy of the gravitational field.

So, that same total energy per unit mass is also the kinetic energy per unit mass required at the surface to get you out to that infinity point. Since KE/m = 1/2 v^2, you can solve for the velocity required for any object to leave the surface and make it to infinity - i.e. it's not in an orbit and it's never coming back.

Answer 5

ESCAPE VELOCITY IS THE VELOCITY WITH WHICH A ROCKET MUST TRAVEL TO ESCAPE THE GRAVITATIONAL PULL OF THE EARTH AND GO IN TO OUTER SPACE.But acceleration is the rate of change of velocity.

Answer 6

commence with acceleration: it quite is the upward thrust in velocity or speed and demands the enter of potential, referred to as tension, to do it. speed is the cost of something in one path. working example, whilst a gun is offered the bullet velocity is termed speed. that's the cost of the bullet travels on the line of the barrel. The results of gravity is excluded. velocity is the entire ... umm ... velocity. The gadget in a vehicle is termed a speedometer, if the automobile is going around a nook the cost maintains to be an analogous even however the speed has replaced.