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Physics question ( mechanics) A level

A lift ascends with a constant acceleration, a, then travels with a constant speed and is finally brought to rest under a constant retardation, a. If the total distance travelled is h and the total time taken is t, show that the time spent travelling at constant speed is
(t ²-4h/a)^1/2
if you draw a speed-time graph it will look like a trapezium. the gradient of the sloping sides is a ( or -a ). let the length of the top be c ( this is the time of constant velocity ). the amount of time before c begins will be ( t - c )/2

the height P can be found because P/{( t - c )/2} = the gradient = a

so P = 2a/ ( t -c )

the area of the trapezium is (c + t ) x P/2 = h...

you should be able to continue.

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