6. Give an example where the instantaneous rate of change equals the average rat
ID: 3199211 • Letter: 6
Question
6. Give an example where the instantaneous rate of change equals the average rate of change. There are many possible answers for this question. You are free to interpret the problem any way you like, as long as it answers exactly the question 7. If the graph of a function d(t), (where t represents time, and d(t) represents the distance a car is on a straight road from the starting point) is a straight line, what does it mean about the car's velocity? 8. The graph below shows a driver's distance from his house as a function of the time of day. Find the approximate velocity of the car at the following times: 9AM, 11:15AM, 2PM, 3:15PM, 4PM, and 5PM. You must explain how you found the answers. 60 50 40 Out(9630 20 10Explanation / Answer
6. The instantaneous rate of change is equal to the average rate of change whenever the rate of change is constant over the period. For example, if a car moves at 20 km/h constant speed, the average rate of change of distance and the instantaneous change of distance is both the same i.e 20.
7. If the graph of a function d(t) is a straight line, where d(t) is on the y axis, and t is on the x-axis, it would mean that the distance has not changed over time which means that the car is not moving.
8. At 9 am : Since, the curve is a straight line at the point, the velocity is 0.
At 11:15 am: Since, the curve is upward sloping, the velocity is around 30 km/ hr. This can be found by 17.5 - 10/(0.25 hrs) = 30
At 2 pm : Since curve is a straight line, velocity is 0.
At 3:15 pm : 66.67 km/ hr. This is because the velocity was constant from 3pm to 3:45pm. It travelled 50 km within the time. So the average velocity will be 50/0.75 hours. = 66.67 km/hr.
At 4 pm: Similarly, velocity = 20 km/hr
At 5 pm = Similarly, velocity = 0 km/hr
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