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Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1
Question 5
Two cars P and Q are moving in the same direction along the same straight horizontal road. Car P is moving with constant speed 25 m s-1. At time t = 0, P overtakes Q... show full transcript
Worked Solution & Example Answer:Two cars P and Q are moving in the same direction along the same straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 5 - 2010 - Paper 1
Step 1
Sketch, on the same axes, the speed-time graphs of the two cars for the period from t = 0 to the time when they both come to rest at the point X.
Answer
To create the speed-time graphs for cars P and Q, we must plot their speeds against time.
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For Car P:
- From t = 0 to t = T, Car P moves at a constant speed of 25 m/s.
- At t = T, Car P begins to decelerate uniformly to rest at X.
- From t = T to t = 25 s, it will gradually decrease to 0 m/s.
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For Car Q:
- For the first 25 seconds, Car Q moves at a constant speed of 20 m/s.
- After 25 seconds, it begins to decelerate uniformly and also comes to rest at point X at the same time as Car P.
The graph will show the following features:
- Both cars start at different speeds.
- The lines for both cars must intersect on the time axis at the point where they both stop at X.
- You will have horizontal lines for constant speeds and sloping lines for deceleration, meeting at the point where both cars stop.
Step 2
Find the value of T.
Answer
To determine T, we use the distances covered by both cars to set up the equations:
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For Car Q:
It travels at 20 m/s for T seconds then decelerates.
Distance covered by Q before deceleration:
Setting this equal to the distance to X:
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For Car P:
It travels at 25 m/s for T seconds then decelerates:
Distance covered by P before deceleration: Setting this equal to 800:
Rearranging gives: By solving these equations, we find that the value of T is 9.