# How to go from acceleration vs time graph to velocity vs time graph?

1. Apr 24, 2013

### physicslover11

1. The problem statement, all variables and given/known data
The figure below shows the acceleration-versus-time graph for a motorcyclist riding along the x-axis. Assume that at t = 0, x = -1 m and v = 2 m/s.

Unless otherwise specified, use the graphical analysis to solve all the questions below. Do not use the kinematic equations or the functional evaluation of the integral, although, if you happen to know these methods, you may use them to check your graphical result.
1) Plot the velocity-versus-time graph for the first 40 s.
2) a) What is the position of the motorcyclist at t = 40 s? b) What is the distance traveled by the motorcyclist in the first 40 s?
3) a) What is the position of the motorcyclist at t = 15 s? b) Using the kinematic equations, find the position of the motorcyclist at t = 15 s. Compare your answer to that obtained in part a).
4) Roughly sketch the position-versus-time graph for the first 40 s.

2. Relevant equations
i know that Δv=aΔt, Δx=vΔt

3. The attempt at a solution

#### Attached Files:

• ###### Screen shot 2013-04-24 at 9.04.17 PM.png
File size:
9 KB
Views:
86
2. Apr 24, 2013

### johnqwertyful

You just find the slope of the velocity graph. Remember, acceleration is the SLOPE of velocity. So from t=0 to t=5, the acceleration is 2. So that means that the velocity graph looks like...?

3. Apr 24, 2013

### physicslover11

but how do i get the slope of the velocity graph if the velocity graph is what im looking for?

4. Apr 24, 2013

### Dick

The value of the acceleration graph is the slope of the velocity graph. That's whatjohnqwertyful was saying.