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A car moves along a horizontal straight road, passing two points A and B - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1
Question 3
A car moves along a horizontal straight road, passing two points A and B. At A the speed of the car is 15 m s⁻¹. When the driver passes A, he sees a warning sign W a... show full transcript
Worked Solution & Example Answer:A car moves along a horizontal straight road, passing two points A and B - Edexcel - A-Level Maths Mechanics - Question 3 - 2008 - Paper 1
Step 1
Sketch, in the space below, a speed-time graph to illustrate the motion of the car as it moves from A to B.
Answer
To sketch the speed-time graph:
- Start at point A (0s, 15 m/s).
- Show a rapid decrease to 5 m/s at time T = 12s (point W).
- From T = 12s to T = 16s, illustrate constant speed at 5 m/s.
- From T = 16s to T = 22s, show the increase in speed from 5 m/s to V m/s with a uniform acceleration slope.
- Maintain the constant speed at V from T = 22s onwards.
Step 2
Step 3
The distance from A to B is 1 km.
Answer
Use the formula for distance:
Let the constant speed be V. The distance covered is given by:
egin{align*}
ext{Distance} & = ext{Distance from A to W} + ext{Distance from W to V} + ext{Distance from V to B}
& = 120 + rac{1}{2}(15 + 5)(12) + V(22) = 1000 ext{ m}
ext{Solving gives: } & rac{1}{2}(15 + 5)(12) = 120 ext{ m},
30 + 11V = 1000 ext{ m}
ext{So, } V & = 28 ext{ m/s}.
ext{Then the value of V is: } \ V = 28.