Calculate the Increased Speed: Caterpillar's Journey from 3 cm/min to ?

To solve this problem, we'll proceed as follows:

Let us begin by calculating the distance covered in the initial phase of the journey:

• Since the caterpillar crawls for 2 minutes at 3 cm per minute, the distance $D_1$ covered is: $D_1 = 3 \times 2 = 6$ cm.

Given that the total distance traveled by the caterpillar is 30 cm, the distance covered after increasing its speed, $D_2$, is:

• $D_2 = 30 - 6 = 24$ cm.

Next, we use the average speed to determine the total time of the entire journey. The average speed formula is given by:

• $\bar{V} = \frac{\text{Total distance}}{\text{Total time}}$
• Thus, the total time $T$ is: $T = \frac{30}{4.412} \approx 6.8$ minutes.

The time taken at the increased speed ($t_2$) is then $t_2 = T - t_1 = 6.8 - 2 = 4.8$ minutes.

Finally, to find the increased speed $V_2$, we use the relationship:

• $V_2 = \frac{D_2}{t_2} = \frac{24}{4.8} = 5$ cm per minute.

Therefore, the caterpillar travels at 5 cm per minute after increasing its speed.