Question

Distinguish between instantaneous rate and average rate.

_____ rate is the rate measured over a given time interval. _____rate is the rate at a single moment in time. in each of the following situations, is the rate measured the instantaneous rate or the average rate?
a. it took the driver 1.5 hours to drive 90 miles, so her speed was 60 miles per hour
- average rate
- instantaneous rate

b. the driver's speed at 6:05 pm was 65 miles per hour but at 6:15 pm she slowed down to 57 miles per hour.
- average rate
- instantaneous rate

Answer 1

The instantaneous rate is the speed at a single moment, while the average rate is calculated over a given time interval. An example of an average rate is driving 90 miles in 1.5 hours. An example of an instantaneous rate is a driver's speed specifically at 6:05 pm before changing speed at 6:15 pm.

Step-by-step explanation:

Difference Between Instantaneous Rate and Average Rate

The instantaneous rate is the rate of a reaction at a single moment in time, similar to the actual speed of a car in an instant, which does not consider the duration over which that speed is maintained. In contrast, the average rate is the rate measured over a given time interval, akin to calculating the average speed of a car for an entire trip by dividing the total distance traveled by the total time taken.

a. Driving 90 miles in 1.5 hours corresponds to an average rate of 60 miles per hour.

b. The driver's speed changing from 65 miles per hour at 6:05 pm to 57 miles per hour at 6:15 pm refers to the instantaneous rate at two separate moments.

Instantaneous speed is always a scalar quantity and does not include direction, while average speed is still a scalar but is calculated over a specified time period.