Final answer:
The instantaneous acceleration at t=11s is calculated by taking the derivative of the velocity function, v(t) = 20t - 5t² m/s, to find the acceleration a(t) = 20 - 10t m/s², and then evaluating at t=11s, resulting in an acceleration of -90 m/s².
Step-by-step explanation:
To find the instantaneous acceleration at t=11s, we need to consider the given velocity function v(t) = 20t – 5t² m/s and differentiate it to get the acceleration function. The derivative of v(t) with respect to time gives us the functional form of the acceleration.
The derivative of 20t is 20, and the derivative of -5t² is -10t. Thus, the acceleration function is a(t) = 20 – 10t m/s². To find the instantaneous acceleration at t=11s, we plug in 11 for t in the acceleration function:
a(11) = 20 – 10(11) = 20 – 110 = -90 m/s²
Therefore, the instantaneous acceleration at t=11s is -90 m/s², indicating that the particle is decelerating at this particular moment in time.