The belt of one ramp moves at a constant speed such that a person who stands still on it leaves the ramp 64 s after getting on. Clifford is in a real hurry, however, and skips the speed ramp. Starting from rest with an acceleration of 0.37 m/s2, he cov- ers the same distance as the ramp does, but in one-fourth the time. What is the speed at which the belt of the ramp is moving?

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wagonbelleville wagonbelleville · Answer 1 · 2020-01-24T10:00:09+01:00

Answer:

0.74 m/s

Explanation:

given,

time taken by the ramp to cover cliff , t = 64 s

acceleration = 0.37 m/s²

distance traveled by the belt

[tex]x = v_{belt}t_{belt}[/tex]

Clifford is moving with constant acceleration

[tex]x = v_ot + \dfrac{1}{2}at^2[/tex]...(1)

initial velocity is equal to zero

[tex]x =\dfrac{1}{2}at^2[/tex]........(2)

equating equation (1) and (2)

[tex]v_{belt}t_{belt}=\dfrac{1}{2}at^2[/tex]

[tex]v_{belt}t_{belt}=\dfrac{1}{2}a(\dfrac{1}{4}\times t_{belt})^2[/tex]

[tex]v_{belt}=\dfrac{1}{32}a t_{belt}[/tex]

[tex]v_{belt}=\dfrac{1}{32}\times 0.37 \times 64[/tex]

[tex]v_{belt}= 0.74\ m/s[/tex]

Speed of the belt is equal to 0.74 m/s