Question

How do velocity and acceleration differ?

Answer 1

See below:

Explanation:

Common calculus problems involve displacement-time functions,
`d(t)`. For the sake of the argument let's use a quadratic to describe our displacement function.

`d(t)=t^2-10t+25`

Velocity is the rate of change of displacement- the derivative of a `d(t)` function yields a velocity function.

`d'(t)=v(t)=2t-10`

Acceleration is the rate of change of velocity- the derivative of a `v(t)` function or the second derivative of the `d(t)` function yields an acceleration function.

`d''(t)=v'(t)=a(t)=2`

Hopefully, that makes their distinction clearer.