# Sketching velocity graph from acceleration graph

I know that the area under an acceleration vs. time graph is the velocity, but how do I use that information to sketch a velocity vs. time graph. Is the area considered the slope for the velocity graph? Also how is it possible for a car to be slowing down during the first half of the motion? Attached is a rough sketch of what the acceleration vs. time graph looks like.

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so on the first thrid of the graph there is constant acceleration so what does this tell you about the velocity?? the middle third there is no acceleration which implies the velocity must be the same. and the last third there is decceleration which implies what about the velocity??

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I know that the area under an acceleration vs. time graph is the velocity, but how do I use that information to sketch a velocity vs. time graph.
You need additional information, such as the initial speed.

Note that in this graph, the acceleration increases to a maximum value, stays at that value, then decreases to zero. (Acceleration is only constant in the middle portion of the graph.) If this graph is accurate, and the car starts from rest, the speed is increasing at all times. Is that what you meant to describe?

so on the first thrid of the graph there is constant acceleration so what does this tell you about the velocity?? the middle third there is no acceleration which implies the velocity must be the same. and the last third there is decceleration which implies what about the velocity??
Actually, your wrong. The first third of the graph is an increasing acceleration. The second third is a constant acceleration, and the last third is a decreasing acceleration.