Velocity-Time Graphs

Velocity-Time Graphs – Key things to remember:

With speed on the y-axis and time on the x-axis, a speed-time graph tells us how someone/something’s speed has changed over a period of time.

1) The gradient of the line = Acceleration
2) Negative gradient = Deceleration
3) Flat section means constant velocity (NOT STOPPED)
4) Area under the graph = Distance travelled

Skill 1: Describing a graph

One Skill you will need learn is describing a velocity time graph.

Example: The speed-time graph shows a 50-second car journey. Describe the 50 second journey.

Step 1: Split the graph up into distinct sections, these can be seen in the image as A, B, C and D.

Step 2: In detail describe each part of the journey, ensuring to use numerical values throughout.

Section A – The car accelerated from 0 to 15 m/s over the first 10 seconds (because the line is straight, the acceleration is constant).

Section B –  The line is flat, meaning the car’s speed did not change for 10 seconds – meaning it was moving at a constant speed.

Section C – The car accelerated up to 25 m/s over the next 10 seconds,

Section D –  Finally it spent the last 20 seconds decelerating back down to 0 m/s.

Skill 2: Calculating Acceleration

Acceleration is calculated as the change in speed over time.

Section \bf{A}:  Acceleration between 0s and 10s = gradient=\dfrac{15-0}{10-0}=1.5 m/s^2

Section \bf{B}: This section is flat, meaning the acceleration will be 0

Section \bf{C}: Acceleration between 20s and 30s = gradient =\dfrac{25-15}{30-20}=1 m/s^2

Section \bf{D}: Acceleration between 30s and 50s = gradient =\dfrac{0-25}{50-30}=\dfrac{-25}{20} = -1.25 m/s^2

Section \bf{A} has the largest acceleration, so the maximum acceleration is 1.5 m/s^2

Note: units of acceleration are expressed in distance/time\bold{^2}, which in this case is m/s\bold{^2}.

Skill 3: Calculating total distance travelled

Calculating the total distance travelled is one of the most common exam questions you may see.

This gives two triangles, a rectangle, and a trapezium, which are all shapes that we can work out the area of.

\text{A}=\dfrac{1}{2}\times10 \times15= 75 m

\text{B}=10\times15=150 m

C=\dfrac{1}{2}(15+25)\times10=200 m

D=\dfrac{1}{2}\times20\times25=250 m

Total distance travelled:

75+150+200+250=675 m

Skill 4: Average of curved graphs

To work out the average acceleration over the 4 seconds, we will draw a line from where the graph is at 0 s to where the graph is at 4 s and find the gradient of it.

So, we get the average acceleration to be,

\text{gradient}=\dfrac{6-0}{4-0}=1.5 m/s^2

Skill 5: Instantaneous gradient of a curve

Then, we get the instantaneous acceleration to be,

\text{gradient}=\dfrac{5.8-3.2}{3.5-1.0} = 1.04 m/s^2 (3 sf).