The mathematical technique used to calculate the area under a graph is integral calculus. This is a complex subject which I am not going to attempt to explain in detail- it normally takes years of study.
The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
It is not, if it is a graph of force against acceleration.
change in velocity
Displacement is the area under the v-t graph.
The distance travelled over the time period represented by the area under the v-t graph between the end points.
The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
It is not, if it is a graph of force against acceleration.
Velocity.
Since jerk is defined as the derivative (the rate of change) of acceleration, in the case of the area under the curve, it is the other way round: the integral (area under the curve) for jerk is the acceleration.
its the velocity
Nothing in particular. It certainly does not represent acceleration.
The distance covered between two points in time is the area under the graph between the two points.
change in velocity
Velocity is NOT the slope of the acceleration vs. time graph. Velocity is the area under the acceleration vs. time graph. Velocity is the slope of a position vs. time graph, though. For you Calculus Junkies, v = the integral of acceleration with respect to time.
You can't. However, you can find the change in speed between two points in time by finding the area under the acceleration-time graph.
A position time graph can show you velocity. As time changes, so does position, and the velocity of the object can be determined. For a speed time graph, you can derive acceleration. As time changes, so does velocity, and the acceleration of the object can be determined.If you are plotting velocity (speed) versus time, the slope is the acceleration.
Derivitives of a velocity : time graph are acceleration and distance travelled. Acceleration = velocity change / time ( slope of the graph ) a = (v - u) / t Distance travelled = average velocity between two time values * time (area under the graph) s = ((v - u) / 2) * t