Final answer:
Instantaneous acceleration is found by taking the derivative of the velocity function v(t) = 20t - 5t², resulting in a(t) = 20 - 10t m/s². This represents the acceleration at any given time during the motion, and it is the rate of change or slope of the velocity-versus-time graph at a specific instant. Negative acceleration indicates deceleration.
Step-by-step explanation:
The value of instantaneous acceleration at a specific instant can be found by taking the derivative of the velocity function with respect to time. For the given function v(t) = 20t - 5t² m/s, the instantaneous acceleration function a(t) is the derivative of v(t) with respect to time t, which is a(t) = dv/dt. Calculating the derivative of v(t), we obtain a(t) = 20 - 10t m/s². This formula gives the acceleration at any time t during the particle's motion.
Instantaneous acceleration is different from average acceleration, which only requires the change in velocity over a given time interval. The distinction is crucial because the magnitude of acceleration can vary with time. However, to find instantaneous acceleration, one must consider the exact rate of change at a particular moment, which is effectively the slope of the velocity-versus-time graph.
It's significant to remember that negative acceleration refers to acceleration that is directed in the negative direction of the chosen coordinate system, also known as deceleration.