Finding velocity and distance with acceleration function

The acceleration function (in m/s^2) and the inital velocity are given for a particle moving along a line. Find:
a) the velocity at time "t"
b) the distance traveled during the given time interval.

a(t)= 2t+3
v(0)= -4
0 (less than or equal to) t (less than or equal to (3)

I have no idea where to even begin yet alone finish this problem. If someone could explain cleary and show me that would be amazing! Thanks for your time.

To answer this question you need to know a bit of calculus.There is a relationship between displacement, velocity and acceleration. Velocity is the derivative of displacement, and acceleration is the derivative of velocity. Therefore, velocity is the integral of acceleration and displacement is the integral of velocity.

You are given a function for acceleration: a(t)= 2t+3
you want to find velocity, so integrate the function for acceleration:
Integral of a(t)= 2t+3 = v(t) = t^2 + 3t + c
v(t) = t^2 + 3t + c

Now to find your constant,c, plug in the point you are given (V(0) = -4)

v(0) = 0^2 + 3(0) + c = -4
c = -4

Now your function for Velocity looks like this:
v(t) = t^2 + 3t - 4
or
v(t) = (t + 4)(t - 1)
I think that's enough for part (a), they have not asked you to find the velocity at a specific time.

For part (b) they are asking you to find a function for displacement, so you must integrate the function for velocity (due to the relationship I explained earlier):
integral of v(t) = t^2 + 3t - 4 = d(t) = (1/3)t^3 + (3/2)t^2 - 4t + c
d(t) = (1/3)t^3 + (3/2)t^2 - 4t + c

Now you have found a function for displacement, but they want the total distance traveled. Because of our function for velocity we know that the particle is still when t = 1 (because velocity is 0 when t = 1, v(t) = (t + 4)(t - 1) ). This means that after one second the particle stops and changes direction. This makes the question more complicated because plugging in (t = 3) in the displacement function wont take into consideration the points at which the particle is still, all it will tell you is how far away from the origin it is.