# How to Lift an object at constant velocity vertically

Let's say there is a Table on the floor . I lift the table up in such a way that it keeps going upwards 5 m/s (I kept holding the table every instant). I lifted the table for 3 seconds so it reached 15 meter height. Now if I just move my hands from the table it just falls downward from that time.

If its velocity was 5 m/s, shouldn't the table go higher until the velocity becomes 0 m/s before the table starts falling down? Did the table really get constant velocity of 5m/s? If not then why? And how can one lift an object at a constant velocity upwards?

1. If the table was moving at 5 m/s, it will decelerate with the gravitational acceleration of roughly $9.81 m/s²$, so it will continue to rise for approximately 0.5 seconds before it starts falling.
2. I am not sure about your second question. If you moved it at constant velocity of 5 m/s, then yes, the table will have this velocity.
3. You could use a motor with a constant angular velocity, like the one discussed here.
• 2nd question was about the fact I am literally pulling the table against gravity. So should not it start accelerating as we know to lift an object against gravity we must pull it with a force > Weight of the object. As the table was at rest and I lifted it up then definitely I had to accelerate it. But at the same time I pulled it such a way it was always in my hand and kept going upwards at the same velocity. How can both be possible. Did I apply force. If so then why it was not accelerating rather than kept moving on constant velocity – ffahim Mar 26 '18 at 12:28
• Alright, I understand. In the beginning, you have to accelerate the table until it reaches 5 m/s. From there, you could theoretically keep the velocity constant. You are right, you cannot jump from 0 to 5 m/s instantly. – lmr Mar 26 '18 at 12:29

"If its velocity was 5 m/s, shouldn't the table go higher until the velocity becomes 0 m/s before the table starts falling down?"

It does just that. You can calculate how much further it goes up after you've let go by using a constant acceleration equation or by using energy conservation. All that matters for this calculation is the body's speed when you let go. Incidentally, 5 m/s is very roughly 10 miles per hour, so it's very fast – for a table!

"Did the table really get constant velocity of 5.0 m/s?"

If you lifted the table 15 m in 3.0 s starting from rest, its mean speed over the 3.0 s would be 5.0 m/s. It would have to spend at least the first part of the 3.0 s at a lower speed, if it had to accelerate from rest. If the acceleration were constant it would be moving at 10 m/s at the end of the 3.0 s.

"And how can one lift an object at a constant velocity upwards?"

You can't, if the object starts from rest. See above. But you could get the initial acceleration over with quickly and then keep the object moving at constant speed (if you're clever enough) for the rest of the 3 s.

• Just think about a pen. U hold it in your hand. Now you lift it each metre at constant speed. Now just free the pen(I mean just move ur hands) see u didn't just throw it upwards. I meant just lifting it upwards forcefully) won't u see it falling as if it's velocity was 0. – ffahim Mar 26 '18 at 12:45
• No. See my answer above. How much further it rises after you've let go depends on its velocity when you release it. It doesn't matter whether or not you are $deliberately$ throwing it upwards. Recommend you do the simple calculation of how far it rises once you've let go. – Philip Wood Mar 26 '18 at 13:00
• @ffahim When you let the pen go, you might accidentally slow it down as your hand slows down just before releasing. Put the pen on you palm without holding it, move it in constant velocity and suddenly stop moving your hands. The pen will rise up – Archisman Panigrahi Dec 11 '18 at 17:24