How does an object's velocity change over time during constant acceleration?

[skm22]

When something is accelerating at a constant rate, each speed on the velocity-time graph is only present at one specific point in time. For example, it might be at 5m/s at 5 seconds. How is that possible? Speed is the change in distance over change in time.

 

[Svein]

Speed is the change in distance over change in time

Yes, usually written $v=\frac{ds}{dt}$.

When something is accelerating at a constant rate, each speed on the velocity-time graph is only present at one specific point in time.

Yes. Acceleration is the change of velocity over change in time, usually written $a=\frac{dv}{dt}$. So, if a is constant, $v=v_{0}+a_{0}\cdot t$ (constant acceleration or deceleration). The standard example: you hold an object at height h and drop it. Then gravity will impose a constant acceleration on it and since it started with velocity 0, you have $v=g\cdot t$ (at least until the object hits the ground).

 

[Quarlep]

I didnt understand your question.Are you asking how can we show velocity as point in velocity-time diagram ? How this is possible ? Is this your question
Svein gave the answer while I was writing.

 

[rolotomassi]

well gravity causes things to accelerate at a constant rate, says ~ 10 m/s^2. What this means is that every second that an object falls under gravity on earth, ignoring air resistance, its velocity increases by 10 m/s. If you drop something from rest its velocity is zero. After 1 second its velocity is 10m/s, 2 seconds its 20m/s. This increase of velocity happens in time. So the object must 'pass through' all of the velocities in order to attain 10 m/s. Then it passes through every velocity from 10 - 20 m/s etc and will keep on doing so until something stop it, like the floor.

While the velocity is only ever one value at on specific time, it does not need to travel any distance at that value for us to assign it say 5m/s and t = 5 seconds. If we remove the force at the instant its velocity it 5 m/s, this will be its velocity indefinitely.