Question

so what would the steps be for finding the acceleration and velocity when x(t)=5t^2+17t?

Answer 1

x(t) describes the position of a given particle. In these cases,velocity is the *rate of change* of position. The rate of change of a function is also known as its derivative.

Answer 2

So, to find the velocity of that particle, you would take the derivative of the position function.

Answer 3

The acceleration of a particle describes the *rate of change* of its velocity -- i.e., how fast it is slowing down or speeding up (vs velocity which is how fast it's going right now). In this case, that means the derivative of the velocity function.

So, first find the derivative of the position function, that'll give you the velocity function. Then, find the derivative of the velocity function, and you'll get the acceleration function.