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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 construct the speed-time graphs for cars P and Q:
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For Car P:
- From t = 0 to t = T, P travels at a constant speed of 25 m/s.
- At t = T, P begins to decelerate uniformly.
- It comes to rest at point X after traveling 800 m.
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For Car Q:
- From t = 0 to t = 25 s, Q travels at a constant speed of 20 m/s.
- Q starts to decelerate at t = 25 s.
- It also arrives at point X at the same time as P.
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The graph will show:
- A horizontal line at 25 m/s for P until T.
- A horizontal line at 20 m/s for Q until 25 s.
- A sloped line downward for both cars after T and 25 s to depict deceleration.
- The graphs will cross and meet the time-axis at the same point corresponding to 800 m traveled.
Step 2
Find the value of T.
Answer
To find T, we set up the equations based on the distances traveled:
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For Car Q:
egin{align*} ext{Distance} &= ext{Average speed} imes ext{Time} \ 800 &= 20 imes rac{T + 25}{2} \ 800 &= 10(T + 25) \ 80 &= T + 25 \ T &= 80 - 25 \ T &= 55 ext{ s} \
ext{For Car P:} \ ext{Distance} &= ext{Average speed} imes ext{Time} \ 800 &= 25 imes rac{T + 55}{2} \ 800 &= 12.5(T + 55) \ 64 &= T + 55 \ T &= 64 - 55 \ T &= 9 ext{ s} \ ext{So, the value of T is} \ extbf{T = 9 seconds.} \end{align*}