COMPOUND MEASUREMENTS
TIP: When doing these sort of problems, remember:
a) Units of length are e.g. centimetres, metres, kilometres, miles etc.
b) Units of mass are e.g. grams, kilograms, ounces, pounds etc.
c) Units of time are e.g. seconds, minutes, hours, days etc.
d) When units are combined we end up with what is called a compund measurement. Speed is a compound measurement:
Speed
= Distance and
can be expressed as metres per second (m/s)
or kilomtres per
Time
hour (km/h)
or miles per hour (normally shortened to mph).
Density is another compund measurement - units are Kg/m3 or g/cm3 etc..
Density
= Mass
Volume
e) Make sure you are familiar with all aspects of Distance-Time Graphs and Velocity-Time graphs as these are quite popular with GCSE examiners.
f) Make sure that your units are consistent when answering questions. If units are not consistent then you will need to convert them to ensure that they are - know how to convert seconds into hours (e.g. number of seconds in 1 hour = 60 x 60) etc.
Solve the following:
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1. At the end of a rally the cars which took first and last place had average speeds of 104 km/h and 96 km/h. The first car took 3 hours 52 minutes to complete the course and the last car took 4 hours 5 minutes to complete the course. Approximately how many kilometres was the last car behind the first car, when the first car crossed the finishing line? |
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2. A car travels along the motorway at an average speed of 112 km/h for 3 hours. The car then travels along minor roads with an average speed of 65 km/h for 2 hours. What is the average speed of the car over the whole journey? |
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3. The diameter of a car wheel is 56cm. When the car is travelling at 110 km/hour, how many revolutions does the wheel make in one minute? |
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4. A long distance lorry driver sets off on a journey with a full tank of diesel (360 litres). When the driver returns to the depot the lorry has travelled 4,638 kilometres. The level of diesel remaining in the tank is checked and the tank is found to have a quarter of a tank of diesel remaining. a) How much diesel was used on the journey? b) What was the average diesel consumption? c) Assuming that the average diesel consumption does not change, how much further can the lorry travel before running out of diesel? |
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5. The diagram below shows a prism which has a mass of 3 kg.
a) Calculate the volume of the prism. b) Calculate the density of the prism in g/cm3 of the material from which it is made. |
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6. A saleswoman travelled by car to see a customer 200 miles away. She set off from home at 8.00am and arrived at the customer's office at noon. a) What was the car's average speed on the outbound journey? b) The petrol in the car cost 0.82p per litre. The car on average will do 35 miles to the gallon. What is the cost of petrol for the whole journey (i.e. outbound and return)? Assume 1 gallon = 4.5 litres |
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7. Greg drives 90 miles to see his grandparents. The distance-time
graph below shows this journey. a) Explain what you think may have happened in the time up to 1 hour and just after 2 hours. b) Calculate Greg's average speed over the whole journey. c) What was Greg's average speed on the return journey?
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8. The diagram below shows the speed-time graph of a non-express
train on its journey from Abbots End station to Newtown station. a) What is the distance between the two stations? b) What was the acceleration of the train before it achieved a constant speed? c) At what rate did the train decelerate before stopping at Newtown station?
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