Question

Mowgli, while trying to escape from Shere Khan, ran 500 metres in 10 seconds to reach near the river and swam 200 metres in 20 seconds before climbing the trees. Then he climbed 100 metres in 10 seconds before finding peace on top of a tree.

Statement: Mowgli’s average speed in this journey is $(\frac{500}{10}+\frac{200}{20})+\frac{100}{10})\times \frac{1}{3}=\frac{70}{3}$ metres per second , which is the averages of speeds.

• A. True
• B. False

Answer 1

The correct option is B

False

Here, we are given a statement saying that the average speed in the total journey is equal to average of speeds. Speed is ratio of total distance travelled and total time taken. Distance travelled by Mowgli is 500+200+100 = 800 metres and time take to cover that distance is 10+20+10 = 40 seconds. So the average speed will be (800/40)=20 m/s. But the average of speeds will be 70/3 as given in the question. So the given statement is wrong. From this we can say that the average rate of change is not equal to averages of rate of changes in general. There could be cases when the average rate of change is equal to average of rate of changes