Velocity-time graphs

The first graph in the diagram above shows a velocity-time graph for a car travelling at a constant velocity. It is not accelerating or decelerating. 

As shown in the second the acceleration is gently increased so the graph slopes upwards.

In the third graph the car accelerates more rapidly, and since its velocity would increase more rapidly the graph would be steeper.  

The acceleration is shown by the slope (gradient) of the velocity-time graph. 

Here the velocity-time graph of a car starting off at one set of traffic lights and stopping at the next set of lights.  Can you see that the car accelerates from A to C, travels at a constant velocity between C and D and then decelerates to stop at E? 

Between which two points is the motor bike accelerating most rapidly? Which part of the graph might show the motorbike travelling at a constant speed?  

When does the rider start braking? Which part of the graph shows the rider hitting a brick wall?

Here is a velocity-time graph of a lift climbing from the ground floor to the top of the building.  

 At which point (A, B or C) is it on the ground? A

At which point is it travelling the fastest?  B

What is its maximum velocity?  10 m/s

How long did it take to reach this velocity? 5 seconds

It decelerates and stops at the top of the building at C.  How long did the journey take?  7 seconds

We can use the slope to find its acceleration:

acceleration = change in velocity/ time taken for the change

acceleration = 10 m/s ÷ 5 s

acceleration = 2 m/s²

Look at each of the lettered sections OA, AB, BC, CD, DE and EF on the speed-time graph.

Images: Harrage, E. (2023). Velocity-time graphs. (CC BY)

a) Choose the correct word from the list below to describe the motion taking place in each section.

acceleration

constant speed

stationary

(i) OA (ii) AB (iii) BC (iv) CD (v) DE (vi) EF

b) At what time during the journey did the bus reach its greatest speed?

c) How long did the bus stop for during its journey?

d) During which section of the journey did the bus have the greatest acceleration?

e) Calculate the acceleration of the bus during section DE.

f) Which section could be described as having a negative acceleration?

Answers:

a) OA - the speed of the bus is changing. Therefore, according to the definition, the bus has an acceleration.

AB - the speed does not change. The bus has a constant speed of 10 m/s.

BC - the bus is slowing down. Its speed is changing. Therefore, according to the definition, the bus has an acceleration.

CD - the speed of the bus is 0 m/s over this section. The bus is stationary.

DE - the speed of the bus is changing. The bus has an acceleration.

EF - the speed does not change. The bus has a constant speed of 5 m/s. 

b) After 5 s.

c) 3 s.

d) BC - this part of the graph has the steepest slope.

e) To find the acceleration in section DE use the formula

$$\frac{\mathrm{<span\; style="font-size:\; 0.9375rem;\; font-family:\; Poppins;"><span\; style="font-size:\; 0.9375rem;"><span\; data-reactid=".18ziugwg252.0.0.0.1:0.1.0.\$0.\$1.\$1.3.\$11.0"> \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; where:</span></span></span>}}{}$$

$$\frac{\mathrm{<span\; style="font-size:\; 0.9375rem;\; font-family:\; Poppins;">a\; =\; 1\; m/s</span><span\; style="font-size:\; 0.9375rem;\; font-family:\; Poppins;"><br></span><span\; style="font-size:\; 0.9375rem;\; font-family:\; Poppins;"><span\; style="font-size:\; 0.9375rem;"><span\; data-reactid=".18ziugwg252.0.0.0.1:0.1.0.\$0.\$1.\$1.3.\$15.0">f)\; BC.\; The\; bus\; is\; slowing\; down,\; so\; it\; has\; a\; negative\; <a\; class="autolink"\; title="Acceleration"\; href="https://www.cenasuportaal.org/opleiding/mod/quiz/view.php?id=705">acceleration</a>.\; This\; type\; of\; <a\; class="autolink"\; title="Acceleration"\; href="https://www.cenasuportaal.org/opleiding/mod/quiz/view.php?id=705">acceleration</a>\; is\; sometimes\; referred\; to\; as\; deceleration.</span></span><br></span>}}{}$$