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On the move

Example questions

If you have revised carefully the definitions and descriptions you should now be ready to tackle two typical examination questions. The questions are designed to test your understanding of average speed, speed (instantaneous speed) and acceleration. See how you get on with each question. Then scroll down to see if you got the answers.

Question

An aircraft on a test flight travels at a steady speed of mach 2 (twice the speed of sound). It travels a measured distance of 1.02 km in 1.5 s during its test flight.

  • a Calculate the average speed of the aircraft in metres per second.
  • b What is the instantaneous speed of the aircraft at all times during the test flight?
  • c Calculate the speed of sound using the information given in the question.
Answer

aYou have to remember the definition of average speed to answer the question.

average speed of aircraft = distance travelled/time taken

Next you have to insert the data into the relationship.

You need to note that the distance given in the question is measured in kilometres. The question asks us to give the average speed in m/s. So you will need convert the distance to metres.

\eqalign{ 1.02 km\; & = & \; 1020 m \cr \cr average\; speed\; of\; aircraft\; & = & {1020 \over 1.5} \cr \cr & = & \; 680 m/s \cr}

b We are told that the aircraft is travelling at a "steady speed". Therefore you should know that at any instant during the test flight its speed has the same value. This value for the speed of the aircraft is just the same as the value you calculated for its average speed. Therefore, the speed at all times during the test flight is 680 m/s.

c You need to read the question carefully to answer this part correctly. In fact you always need to read a question carefully! You are told that the aircraft is flying at twice the speed of sound. Therefore the value calculated for the speed of the aircraft is double the speed of sound.

\eqalign{ speed\; of \;aircraft\; & = & \; 2 \times \;speed\; of\; sound \cr \cr speed\; of\; sound\; & = & {680 \over 2} \cr \cr & = & \; 340 m/s \cr}

Question

A car starts from rest and reaches a speed of 20 m/s in a time of 4 s.

  • a What is the initial speed of the car?
  • b What is the change in speed of the car during the 4 s period?
  • c What is the acceleration of the car during this time?
Answer

a The question tells us that that the car is initially at rest. Therefore its initial speed is 0 m/s.

b The final speed after 4 s is 20 m/s.

    • The change in speed of the car = final speed − initial speed
      • = 20 − 0
      • = 20 m/s

c

\eqalign{ acceleration\; of \;the\; car \; & = & \; {change \;in\; speed \over time\; taken} \cr \cr & = & {20 \over 4} \cr \cr & = & \; 5 m/s^2 \cr}

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