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A car is moving along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 4 - 2007 - Paper 1
Question 4
A car is moving along a straight horizontal road. At time t = 0, the car passes a point A with speed 25 m s⁻¹. The car moves with constant speed 25 m s⁻¹ until t = 1... show full transcript
Worked Solution & Example Answer:A car is moving along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 4 - 2007 - Paper 1
Step 1
Sketch a speed-time graph to show the motion of the car from A to B.
Answer
To sketch the speed-time graph, we identify the following points:
- From t = 0 to t = 10 s, the speed is constant at 25 m/s.
- From t = 10 s to t = 18 s, the car decelerates.
- At t = 18 s, the speed is V m/s.
- From t = 18 s to t = 30 s, the speed remains constant at V m/s.
The graph consists of two horizontal lines (at 25 m/s and V m/s) and a sloping line between 10 s and 18 s, indicating uniform deceleration.
Step 2
the value of V
Answer
To find V, we use the equation for distance:
Total distance travelled = Distance from A to B = 526 m.
The distance during three intervals is:
- From 0 to 10 s:
distance = speed × time = 25 m/s × 10 s = 250 m.
- From 10 s to 18 s (deceleration): Let the deceleration be a m/s². The average speed during this phase is
Distance = Average Speed × time =
- From 18 s to 30 s: Distance = Speed × Time = V × 12.
Combining these:
Solving this equation leads to V = 11 m/s.
Step 3
the deceleration of the car between t = 10 s and t = 18 s.
Answer
To calculate the deceleration (a), we use the formula for final velocity:
Where:
- V = final velocity = 11 m/s
- u = initial velocity = 25 m/s
- t = time = 8 s
Rearranging gives:
Solving for a:
Thus, the deceleration of the car is 1.75 m/s².