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A car is moving along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 4 - 2008 - Paper 1
Question 4
A car is moving along a straight horizontal road. The speed of the car as it passes the point A is 25 m s⁻¹ and the car maintains this speed for 30 s. The car then d... show full transcript
Worked Solution & Example Answer:A car is moving along a straight horizontal road - Edexcel - A-Level Maths Mechanics - Question 4 - 2008 - Paper 1
Step 1
Sketch, in the space below, a speed-time graph to show the motion of the car from A to B.
Answer
To sketch the speed-time graph:
- Mark the vertical axis as speed (m s⁻¹) and the horizontal axis as time (s).
- Plot the initial point A: at time 0 s, speed = 25 m s⁻¹.
- Draw a horizontal line from 0 s to 30 s, maintaining the speed of 25 m s⁻¹.
- At 30 s, the car begins to decelerate uniformly to 10 m s⁻¹ over an unspecified time period. Assume it takes 8 seconds to reach the new speed (calculated in part b).
- Draw a straight line decreasing from 25 m s⁻¹ at 30 s to 10 m s⁻¹ at 38 s.
- After 38 s, draw a horizontal line from 38 s to 90 s, showing a constant speed of 10 m s⁻¹.
Step 2
Calculate the deceleration of the car as it decelerates from 25 m s⁻¹ to 10 m s⁻¹.
Answer
To calculate the deceleration:
- Initial speed, m s⁻¹, final speed, m s⁻¹.
- The time taken to decelerate, s (from the time calculated in the graph sketch).
- Use the formula for deceleration:
- Substituting the values: .
- Therefore, the deceleration of the car is 1.875 m s⁻².