Distance= _t_1t_2|v|, dt speed= distancet_2-t_1 (t_2>t_1) Find direction changes from v = 0 and a sign check. Evaluate displacement at the endpoints and each direction change, then add the absolute changes. Motion diagram Change in displacement=-3-0=-3 =5+8=13 **Quantity** | **How to find it** Change in displacement from 0 to n | s(n)-s(0) or _0n v,dt Distance travelled in the nth second | |s(n)-s(n-1)| (split further if the particle rests inside that second) Total distance in the first n seconds | Split at every rest time; add |change in s| for each stage Average speed | total distancetotal time Instantaneous speed | |v| at that instant For the nth second use n − 1 to n, splitting again if direction changes. A rest time with no direction change needs no split.

\(\text{Distance}=\int_{t_1}^{t_2}|v|\,\mathrm dt\qquad\text{Average speed}=\dfrac{\text{distance}}{t_2-t_1}\quad(t_2>t_1)\)

Find direction changes from v = 0 and a sign check. Evaluate displacement at the endpoints and each direction change, then add the absolute changes.

\(\text{Change in displacement}=-3-0=-3\qquad\text{Distance}=5+8=13\)

Change in displacement from \(0\) to \(n\)

\(s(n)-s(0)\) or \(\displaystyle\int_0^n v\,\mathrm{d}t\)

\(\left|s(n)-s(n-1)\right|\) (split further if the particle rests inside that second)

Total distance in the first \(n\) seconds

Split at every rest time; add \(\left|\text{change in }s\right|\) for each stage

\(\dfrac{\text{total distance}}{\text{total time}}\)

For the nth second use n − 1 to n, splitting again if direction changes. A rest time with no direction change needs no split.

Total Distance, Average Speed and Motion Diagrams

Total Distance, Average Speed and Motion Diagrams