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Today Puzzle #600

Puzzle No. 600– Wednesday 30 October

Over the weekend our Science correspondent Jonathan Amos reported that the Bloodhound supersonic car has completed its first drive across the Hakskeen dry lake in South Africa. The desert floor has been painted to mark out a 10 mile long track and Andy Green intends to drive the car at 800mph in 2020. If he spends ¼ of the time accelerating at a constant rate, ½ the time travelling at top speed, and ¼ of the time decelerating at a constant rate, how long will the journey take?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution

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Consider the total journey time to be T in hours. The final speed 800 mph is achieved at time T/4. Therefore 800 = a x T/4 where a is the rate of acceleration.

The total journey of 10 miles can be written as 10 = 800 x T/2 + 2 x (½) x a x (T/4)2

Substituting 800 = a x T/4 into the second expression we find that 10 = 400 x T + 200 x T = 600 x T

T = 10/600 hr = 1/60 hr = 1 min

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