Determining acceleration

The speed-time graph in the question below shows how the speed of a bus changes during part of a journey.

Question
speed against time: O origin; A time 5 s speed 10 m/s; B time 10 s speed 10 m/s; C at time 12 s speed 0; D time 16 s speed 0; E time 21 s speed 5 m/s; F time 25 s speed 5 m/s

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

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?

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 10m\,s^{-1}.

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^{-1} 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^{-1}.

b) After 5s

c) 3s

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

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

a = \frac{{v - u}}{t}

where a= acceleration, v = final speed, u = initial speed and t = time to change speed

a = \frac{{5 - 0}}{5}

a = \frac{5}{5}

a = 1\,m\,s^{-2}

f) BC. The bus is slowing down so it has a negative acceleration. This type of acceleration is sometimes referred to as deceleration.