(a) A tram moved upward 9 meters per second for 18 seconds. What was the total change in the tram's elevation? (b) In a lab, a substance was cooled by 24 °C over a period of 4 hour... (a) A tram moved upward 9 meters per second for 18 seconds. What was the total change in the tram's elevation? (b) In a lab, a substance was cooled by 24 °C over a period of 4 hours at a constant rate. What was the change in temperature each hour?
Understand the Problem
The question is asking us to calculate the total elevation and change in temperature based on given rates and durations. The first part involves finding the distance traveled by the tram in a certain time, while the second part involves calculating the average temperature change per hour over a cooling period.
Answer
(a) 162 meters (b) 6 °C
Answer for screen readers
(a) The total change in the tram's elevation is ( 162 ) meters.
(b) The change in temperature each hour is ( 6 , \text{°C} ).
Steps to Solve
- Calculate the elevation of the tram
To find the total elevation change, use the formula: $$ \text{Distance} = \text{Speed} \times \text{Time} $$
Here, the speed is 9 meters per second and the time is 18 seconds. Thus, we calculate: $$ \text{Distance} = 9 , \text{m/s} \times 18 , \text{s} $$
- Perform the calculation for elevation
Now, perform the multiplication: $$ \text{Distance} = 162 , \text{meters} $$
This is the total change in the tram's elevation.
- Calculate the temperature change per hour
Next, we find the average change in temperature over 4 hours. The formula to calculate the per-hour change is: $$ \text{Change per hour} = \frac{\text{Total Change}}{\text{Total Time}} $$
Here, the total change is 24 °C and the total time is 4 hours. Thus, we calculate: $$ \text{Change per hour} = \frac{24 , \text{°C}}{4 , \text{hours}} $$
- Perform the calculation for temperature change
Now, perform the division: $$ \text{Change per hour} = 6 , \text{°C/hour} $$
This is the change in temperature each hour.
(a) The total change in the tram's elevation is ( 162 ) meters.
(b) The change in temperature each hour is ( 6 , \text{°C} ).
More Information
For the tram's elevation, the calculation shows the total distance covered in an upward direction over the specified time at a constant speed. For the temperature change, dividing the total cooling by the number of hours gives the average cooling rate per hour.
Tips
- A common mistake is to confuse speed and time, leading to incorrect distance calculations.
- Another mistake is not dividing the total temperature change by the correct time frame, resulting in miscalculated changes per hour.
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