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A level mechanics help needed

Hi, I’ve been trying to do this question as part of my revision but I’m extremely stuck, could someone pls help, thank you :smile:

A speedboat travels from 𝑃 to 𝑄, a distance of 25 000 metres, taking 2000 seconds. The journey has three stages. In the first stage, the boat starts at rest from 𝑃 and accelerates uniformly until it reaches a speed of 𝑉 m s−1. It then continues at this speed for the second stage of the journey, which lasts for half the time of the entire trip. During the final stage of the journey, the boat decelerates uniformly until it stops at 𝑄.

Find the value of 𝑉.
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Pangol
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Original post by champagnevstudy
Hi, I’ve been trying to do this question as part of my revision but I’m extremely stuck, could someone pls help, thank you :smile:

A speedboat travels from 𝑃 to 𝑄, a distance of 25 000 metres, taking 2000 seconds. The journey has three stages. In the first stage, the boat starts at rest from 𝑃 and accelerates uniformly until it reaches a speed of 𝑉 m s−1. It then continues at this speed for the second stage of the journey, which lasts for half the time of the entire trip. During the final stage of the journey, the boat decelerates uniformly until it stops at 𝑄.

Find the value of 𝑉.


Do you know anything about velocity-time graphs, and what the area under such a graph represents? That will help you out here. Don't worry that you don't know how long the first acceleration takes, call the time it takes t. You should then be able to work out an expression for how long the final deceleration takes, in terms of t.

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