A car traveling 36 mi/h accelerates uniformly for 5.4 s, covering 595 ft in this time. What was its acceleration? Round your

Question

A car traveling 36 mi/h accelerates uniformly
for 5.4 s, covering 595 ft in this time.
What was its acceleration? Round your
answer to the nearest 100th place.
Answer in units of ft/s.

in progress 0
Diễm Thu 6 months 2021-07-17T23:19:53+00:00 1 Answers 2 views 0

Answers ( )

    0
    2021-07-17T23:21:28+00:00

    First convert from mi/h to ft/s. There are 5280 ft to 1 mi, and 3600 s to 1 h, so

    36 mi/h = (36 mi/h) * (5280 ft/mi) * (1/3600 h/s) = 52.8 ft/s

    Let a be the acceleration of the car. The car’s speed at time t is

    v = 52.8 ft/s + a t

    so that after 5.4 s, it attains a speed of

    v = 52.8 ft/s + (5.4 s) a

    Recall that

    v² – u² = 2 ax

    where u is the car’s initial velocity and ∆x is the distance it’s traveled.

    We have

    (52.8 ft/s + (5.4 s) a)² – (52.8 ft/s)² = 2 a (595 ft)

    Omitting units, this equation reduces to

    (52.8 + 5.4 a)² – 52.8² = 1190 a

    ==>  29.16 a² – 619.76 a = 0

    ==>  29.16 a – 619.76 = 0

    ==>  29.16 a = 619.76

    ==>  a ≈ 21.25 ft/s²

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )