How would I convert a displacement-time graph to a velocity-time graph? (AS Physics)?

Answer 1

The slope of an S-T graph (distance time) is the average velocity between the time points (t0 and t1) on the S-T graph. Thus, V(t0,t1) = (S1 - S0)/(t1 - t0); where t0 < t1 and S1 is a distance point at t1 and S0 is a distance point at t0 on your S-T graph.

Measure the slopes (V(t0,t1)) in small increments of t1 - t0 along the curve you have in your S-T graph. Plot each slope on your V-T graph, but put each velocity data point mid-way between the time increments. For example, suppose you have S1 = 88 feet at t1 = 2 sec, S0 = 0 feet at t0 = 0 sec. Then V(t0,t1) = (S1 - S0)/(t1 - t0) = 88 ft/2 sec = 44 ft/sec

On the V-T graph, you should put the 44 ft/sec at t = 1 sec, not 0 or 2 seconds, because 44 ft/sec is the average velocity over the two second span and that average occurred halfway between zero and two seconds.

Smaller time increments (t1 - t0) will give you more accurate results. On the flip side, really small increments would take a very long time to plot out on your V-T graph.

By the way, the short cut to all this is to learn differential calculus so you can calculate velocity at any point in an S-T curve. But barring calculus, mapping the S-T to V-T works just fine for most work requirements.

Answer 2

You need to know the equation of the displacement-time graph.
The the gradient to this curve at any point is the velocity at that point in time. The gradient of a curve is obtained by differentiating the equation of the curve, that is find dy/dx. The equation you obtain is the equation of the corresponding velocity time- graph. If you have to plot it then draw up a table of values for y (now the velocity) from the corresponding values of x (time).
Obviously you chose the values of time from those that were used in the original displacement-time graph.

Answer 3

Velocity is the first deriative of displacement with respect to time so you'd differentiate the displacement. If you just have the graph and not data/equation you'll need to determine the slope of the curve at each point and that will give you the velocity.

Answer 4

a million. Mr Laudari is accelerating from t = 0 to t = 2 s and from t = 11 to t = 14 s. 2. Mr Laudari's velocity is persevering with from t = 2 to t = 5 s and from t = 9 to t = 11 s. 3. Mr Laudari decelerates from t = 5 to t = 8 s and from t = 8 to t = 9 s. 4. Distance traveled by using Mr Laudari in first 5s = section under the graph as much as 5s = component to the trapezium ending at t =5s = a million/2 x (5 + 3) x 4 = sixteen m 5. Displacement of Mr Laudari in first 7s = section under the graph as much as 7s = component to the trapezium ending at t =7s = a million/2 x (7 + 3) x 4 = 20 m

Answer 5

Plot the derivative of the displacement-time graph. You can then get acceleration-time graph by plotting the derivative of the velocity-time graph.