# A particle is moving along a straight line and the acceleration is given by a(t)=3t+5, (units m/s2). a)Find v(t) , the velocity at time t if the initial velocity is v(0) = -4 ft/s? b)Find the total distance traveled during the time interval [0, 2]?

##### 1 Answer

Part a):

Part b):

#### Explanation:

Note: I apologize in advance for the long solution; I am not sure how much one who reads this understands and have attempted to give some explanation for each step taken. Hope this helps!

Let's begin by writing out what we are given:

Before we begin to solve the problem, we need to convert acceleration and velocity into some common unit. In this solution, we will be using SI (

Since

Remember that

Integrating both sides, we have:

So,

Applying the above formula, we can find

Here, we must remember how to integrate a polynomial:

Since

Since we are given that

Therefore,

To answer part b), we use the

However, we can take a shortcut and notice that in the quadratic, both the

Here, we need to remember that

Since we have that

Using the Fundamental Theorem of Calculus, we have that:

Plugging this into a calculator we have: