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NemiM [27]
3 years ago
6

a freight train travels at v=60(1-e^-t) ft/s, where t is the elapsed time in seconds. Determine the distance traeled in tree sec

onds, and the acceleration at this time.
Physics
1 answer:
lesantik [10]3 years ago
7 0

Answer

given,

v = 60(1-e^{-t})\ ft/s

t = 3 s

we know,

v = \dfrac{dx}{dt}

a = \dfrac{dv}{dt}

position of the particle

dx = v dt

integrating both side

\int dx =\int 60(1-e^{-t}) dt

x = 60 t + 60 e^{-t}

Position of the particle at t= 3 s

x = 60\times 3+ 60 e^{-3}

 x = 182.98 ft

Distance traveled by the particle in 3 s is equal to 182.98 ft

now, particle’s acceleration

a = \dfrac{dv}{dt}

a = \dfrac{d}{dt}60(1-e^{-t})

  a = 60 e^{-t}

at t= 3 s

  a = 60 e^{-3}

    a = 2.98 ft/s²

acceleration of the particle is equal to 2.98 ft/s²

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