Integrating Kinematics for Velocity from Acceleration: A Simplified Approach

[yup790]

When you want to get velocity from accelleration i have been told you integrate.

Howver v=at and so surley you can just multiply each term in the accelleratin expression by t.

ie:
a=4-0.2t

Surley you can just:
v=(4-0.2t)t
v=4t-0.2t²

 

[hilbert2]

The equation v=at is for the situation when the acceleration is a constant. If it is a function of t, you have to integrate. In that case the corresponding equation is dv=a(t)dt, which gives the infinitesimal change in velocity, dv during infinitesimal time interval dt when the acceleration function a(t) is known. When integrating over a finite time interval, you effectively add a large number of small velocity changes dv to get the total change in velocity, Δv.

 

[yup790]

Thank you. Is there any proof for this. I learn better when I understand the theory behind a topic.