# What is the acceleration of the runner?

acceleration from a curved line on a distance-time graph

## Homework Statement

how do i work out the acceleration from a curved line on a distance-time graph?

## The Attempt at a Solution

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tiny-tim
Homework Helper
welcome to pf!

hi bee-gee! welcome to pf!
how do i work out the acceleration from a curved line on a distance-time graph?

you obviously know how to find the speed (from the slope of [STRIKE]area under[/STRIKE] the graph)

i suppose you could use that to draw a speed-time graph, and then measure the slope of [STRIKE]area under[/STRIKE] that

alternatively, if you can measure the radius of curvature, r, and if you know about centripetal acceleration, then you can do it by imagining that the graph represents a rocket rising vertically …

now put the rocket in a constant horizontal wind, so that sideways distance is proportional to time: if you get the constant right, the vertical-horizontal distance-distance graph will look exactly the same as the original distance-time graph, and you know the total acceleration is purely vertical

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hi bee-gee! welcome to pf!

you obviously know how to find the speed (from the area under the graph)

Isn't speed the slope of a distance / time graph?

tiny-tim
Homework Helper
oops!

oops!

i typed too quickly!

thanks, i'll edit it

HallsofIvy