as a particle moves along a straight path its speed v incm/sce at time t in sec is given by the equation. For what subintervals of the given time interval [a,b] will its speed beatleast k cm/sec? v=t^4 -4t^2 +10[1,6]k=10

garzettaiy

garzettaiy

Answered question

2022-09-01

as a particle moves along a straight path its speed v incm/sce at time t in sec is given by the equation. For what subintervals of the given time interval [a,b] will its speed beatleast k cm/sec?
v = t 4 4 t 2 + 10 [ 1 , 6 ] k = 10

Answer & Explanation

Bryce Obrien

Bryce Obrien

Beginner2022-09-02Added 8 answers

The particles speed will be at least k(10) in the sub interval[2,6].
Since the v has to be at least k,then anything greater than 10 is part of the sub interval. So wejust plug 10 into the equation and solve.
t 4 4 t 2 + 10 = k
t 4 4 t 2 + 10 = 10
t 4 4 t 2 = 0
t 2 ( t 2 4 ) = 0
t 2 4 = 0
t 2 = 4
t = ± 2
-2 is not part of the interval, therefore 2 isthe answer here
Everything greater than +2 in the interval ispart of the sub interval greater than or equal to k =10.

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