Question

The motion of a particle is given by the formula s=−8t3+9t2+80. Determine the acceleration of the particle when t=5.5 s. Acceleration in m/s2= Round your answer to 2 decimal places.

Answer 1

Step-by-step explanation:

To find the acceleration of the particle, we need to find the second derivative of the position equation.

Taking the first derivative of the position equation with respect to time t, we get:

v = ds/dt = -24t^2 + 18t

Now, taking the second derivative of the position equation with respect to time t, we get:

a = dv/dt = d²s/dt² = -48t + 18

To find the acceleration when t = 5.5 s, we substitute t = 5.5 into the acceleration equation:

a = -48(5.5) + 18 = -264 + 18 = -246 m/s²

Rounded to 2 decimal places, the acceleration of the particle when t = 5.5 s is -246.00 m/s².