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sineoko [7]
3 years ago
11

A particle moves along the x-axis so that its velocity at anytime is t greater than or equal to 0 is given by v(t)=1-sin(2pi t)

Physics
1 answer:
UkoKoshka [18]3 years ago
5 0
A) We differentiate the expression for velocity to obtain an expression for acceleration:
v(t) = 1 - sin(2πt)
dv/dt = -2πcos(2πt)
a = -2πcos(2πt)

b) Any value of t can be plugged in as long as it is greater than or equal to 0. 

c) we integrate the expression of velocity to find an expression for displacement:
∫v(t) dt = ∫ 1 - sin(2πt) dt
x(t) = t + cos(2πt)/2π + c
x(0) = 0
0 = = + cos(0)/2π + c
c = -1/2π
x(t) = t + cos(2πt)/2π -1/2π
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final point. The point where the proton is stopped (v = 0)

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where the potential is

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Let us consider that all the charge of the nucleus is in the center, therefore r is the distance from this point to the proton that is approaching

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