# Calculalting displacement, distance and acceleration

1. Jun 29, 2009

hello, i was wondering how i can find the distance travelled by an object in a velocity vs time graph, whilst the line being half a parabola concave up. Inregards to that how can i find acceleration and average velocity (just the formula's). i know in a constant velocity line acceleration is equal to acceleration, i just don't know how to find acceleration on a curved line. (just a gues, would you need to draw a tangent on a point of the line, and hence find the gradient of that line?)

thankyou :)

2. Jun 29, 2009

### Pengwuino

The distance traveled will simply be the integral of the velocity. In the case where you only have a graph, you'll need to estimate the integral using say, Riemann sums.

The instantaneous acceleration is simply the derivative of the velocity, that is the slope at any instance. The average velocity, is simply the final velocity - initial velocity divided by the time interval.

acceleration is equal to acceleration? The instantaneous acceleration of any point is the slope of the line at that point.

3. Jun 29, 2009