contestada

A particle travels along the x-axis so that its position, in centimeters, after t seconds is given by the function
x(t) = –4t^3 – 8t^2 + 16t – 64. What is the acceleration of the particle at time t = 1 sec?

A particle travels along the xaxis so that its position in centimeters after t seconds is given by the function xt 4t3 8t2 16t 64 What is the acceleration of th class=

Respuesta :

LammettHash

Acceleration measures the rate of change of velocity measures the rate of change of position. In other words, the acceleration of the particle is given by the second derivative of its position function.

x(t) = -4t³ - 8t² + 16t - 64

⇒   x'(t) = -12t² - 16t + 16

⇒   x''(t) = -24t - 16

When t = 1, the particle's acceleration is

x''(1) = -24 - 16 = -40

or with proper units, -40 cm/s².

Otras preguntas