Final answer:
Average acceleration is the change in velocity over a period, while instantaneous acceleration is at a specific instant. A car's acceleration sign is positive with increasing speed and negative with decreasing speed in the positive x direction. Acceleration calculations for a racehorse and decelerating car yield 8.33 m/s² and -0.20 m/s², respectively.
Step-by-step explanation:
Similarities and Differences Between Average Acceleration and Instantaneous Acceleration
Average acceleration and instantaneous acceleration are both terms used to describe how an object's velocity changes over time. Average acceleration is calculated by taking the change in velocity divided by the total time period for the motion. It represents the constant rate at which velocity changes over the time interval. Instantaneous acceleration, on the other hand, refers to the acceleration at a particular instant within a time interval and can vary throughout the motion. It is derived from the slope of a velocity-time graph at any given point.
Sign of Acceleration for a Car Moving Along the X-Axis
(a) If the car is moving in the positive x direction with increasing speed, then the sign of the car's acceleration is positive.
(b) If the car is moving in the positive x direction with decreasing speed, then the sign of the car's acceleration is negative (often referred to as deceleration).
Calculation of Average Acceleration for a Racehorse
The average acceleration of a racehorse that accelerates from rest to a velocity of 15.0 m/s due west in 1.80 seconds is calculated using the formula a = (v_f - v_i) / t. Here, v_f = 15.0 m/s, v_i = 0 m/s (at rest), and t = 1.80 s, yielding an average acceleration of 15.0 m/s divided by 1.80 s, which equals 8.33 m/s² due west.
Calculation of Acceleration for a Decelerating Car
A car that decelerates and stops over 5.0 seconds starting from 1 m/s has an acceleration of (0 m/s - 1 m/s) / 5.0 s = -0.20 m/s².