Question
1. The motion of a particle is defined by the function 𝑥 = 12𝑡^3 − 18𝑡^2+2𝑡+5, where x and t are expressed in meters and seconds respectively. Determine the position and velocity when the acceleration is equal to 0.
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Answer to a math question 1. The motion of a particle is defined by the function 𝑥 = 12𝑡^3 − 18𝑡^2+2𝑡+5, where x and t are expressed in meters and seconds respectively. Determine the position and velocity when the acceleration is equal to 0.
Darrell
4.5100 Answers
Dado 𝑥 = 12𝑡^3 − 18𝑡^2 + 2𝑡 + 5, la velocidad se define como el cambio de posición a lo largo del tiempo. eso es:
dx/dt.
Paso 1: Resuelva la función que define la velocidad de la partícula.
dx/dt = velocidad (v) = 36t^2 - 36t + 2
Paso 2: Resuelva la función que define la aceleración de la partícula.
dv/dt = d^2(x)/dt^2 = aceleración (a) = 72t-36.
Paso 3: Resuelva para el momento en que a = 0.
a = 0 = 72t - 36
t = 1/2 segundo
Paso 4. Sustituye t en las ecuaciones que definen la posición y la velocidad.
x = 3
v = -7
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