How can distance be found on a speed time graph?

Answer 1

Instantaneous speed at time t can be found by calculating the derivative of the distance function at time t. This is the same as finding the slope of the line which is tangent to (i.e. intersects at only one point) the distance graph at time t.

If you can describe the distance as a function, then you can find the function for speed by taking the derivative of the entire equation. Similarly, you can find the acceleration by taking the derivative of the speed function. For instance, if the distance x with respect to time t is:

x(t) = 5t^3

then the velocity v with respect to time t would be:

v(t) = x' = 15t^2

and the acceleration a with respect to time t would be:

a(t) = v' = x'' = 30t

So, from that we can figure out the distance, speed, and acceleration at any time t just from the distance graph. For instance, at time t=10, we know that the distance is:

x(10) = 5*10^3 = 5000 meters

and the speed is:

v(10) = 15*10^2 = 1500 meters per second

and the acceleration is:

a(10) = 30*10 = 300 meters per second squared

Answer 2

Distance = Area under the graph.