Suppose a constant force of magnitude F acts on a particle of mass m initially at rest. (a) Integrate the formula for the acceleration found in Problem 14 to show that the speed of the particle after time t is given by (F/m)t (F/m)÷t² +o (b) Rearrange this equation to express the time t as a function of v/c. If the particle's initial acceleration at time t = 0 is a = g = 9.80 m s-2, how much time is required for the particle to reach a speed of v/c = 0.9? v/c = 0.99? v/c = 0.999? v/c = 0.9999? v/c = 1? Required acceleration formula, F a = (F• v), ymc ym
Suppose a constant force of magnitude F acts on a particle of mass m initially at rest. (a) Integrate the formula for the acceleration found in Problem 14 to show that the speed of the particle after time t is given by (F/m)t (F/m)÷t² +o (b) Rearrange this equation to express the time t as a function of v/c. If the particle's initial acceleration at time t = 0 is a = g = 9.80 m s-2, how much time is required for the particle to reach a speed of v/c = 0.9? v/c = 0.99? v/c = 0.999? v/c = 0.9999? v/c = 1? Required acceleration formula, F a = (F• v), ymc ym
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Transcribed Image Text:Suppose a constant force of magnitude F acts on a particle of mass m initially at rest.
(a) Integrate the formula for the acceleration found in Problem 14 to show that the speed of the
particle after time t is given by
(F/m)t
(F/m)²t² +c²°
(b) Rearrange this equation to express the time t as a function of v/c. If the particle's initial
acceleration at time t = 0 is a = g = 9.80 m s-2, how much time is required for the particle to
reach a speed of v/c = 0.9? v/c = 0.99? v/c = 0.999? v/c = 0.9999? v/c = 1?
Required acceleration formula,
F
a =
V
(F. v),
ym
ymc
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