Question

Which graph set-up would enable students to calculate instantaneous acceleration from the slope on the graph? a) Place distance on the x-axis and time on the y-axis b) Place time on the x-axis and distance on the y-axis c) Place speed on the x-axis and distance on the y-axis d) Place time on the x-axis and velocity on the y-axis

Answer 1

Instantaneous acceleration is defined as rate of change in velocity

it is given by the equation

$a = \frac{dv}{dt}$

so here it shows that acceleration is always depends on change in velocity with time and now if we required this change in velocity with time for a small instant of time then it will be given by the slope of velocity and time graph.

So here the graph must be like this to find the slope of any graph we always use the concept that for any graph between y and x we use

$slope = \frac{dy}{dx}$

if we compare it with the formula of acceleration above

then on Y axis we must have to draw the speed and on x axis we must have to draw the time

so correct answer must be

d) Place time on the x-axis and velocity on the y-axis