Problem Analysis:
The given speed-time graph describes the motion of a car traveling between two sets of traffic lights. The graph shows three distinct phases:
1.
Acceleration phase (0 to 10 seconds): The car accelerates from 0 m/s to 16 m/s.
2.
Constant speed phase (10 to 20 seconds): The car travels at a constant speed of 16 m/s.
3.
Deceleration phase (20 to 25 seconds): The car decelerates from 16 m/s to 0 m/s.
We are tasked with:
1. Calculating the deceleration of the car during the last 5 seconds of the journey.
2. Calculating the average speed of the car over the entire journey.
---
Solution:
####
(i) Calculate the deceleration of the car for the last 5 seconds of the journey.
Step 1: Identify the relevant data for the deceleration phase.
- Initial speed at \( t = 20 \) seconds: \( u = 16 \) m/s
- Final speed at \( t = 25 \) seconds: \( v = 0 \) m/s
- Time interval for deceleration: \( \Delta t = 25 - 20 = 5 \) seconds
Step 2: Use the formula for deceleration.
Deceleration is the rate of change of velocity with respect to time, given by:
\[
a = \frac{v - u}{\Delta t}
\]
Substitute the known values:
\[
a = \frac{0 - 16}{5} = \frac{-16}{5} = -3.2 \, \text{m/s}^2
\]
Step 3: Interpret the result.
The negative sign indicates that the car is decelerating. The magnitude of the deceleration is \( 3.2 \, \text{m/s}^2 \).
Final Answer for (i):
\[
\boxed{-3.2 \, \text{m/s}^2}
\]
---
####
(ii) Calculate the average speed of the car between the two traffic lights.
Step 1: Recall the formula for average speed.
The average speed is given by:
\[
\text{Average speed} = \frac{\text{Total distance traveled}}{\text{Total time taken}}
\]
Step 2: Calculate the total distance traveled.
The total distance traveled is the area under the speed-time graph. We can break this into three regions:
1.
Triangle (0 to 10 seconds):
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 16 = 80 \, \text{m}
\]
2.
Rectangle (10 to 20 seconds):
\[
\text{Area} = \text{base} \times \text{height} = 10 \times 16 = 160 \, \text{m}
\]
3.
Triangle (20 to 25 seconds):
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \times 16 = 40 \, \text{m}
\]
Step 3: Sum the areas to find the total distance.
\[
\text{Total distance} = 80 + 160 + 40 = 280 \, \text{m}
\]
Step 4: Determine the total time taken.
The total time is the duration from \( t = 0 \) to \( t = 25 \) seconds:
\[
\text{Total time} = 25 \, \text{s}
\]
Step 5: Calculate the average speed.
\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{280}{25} = 11.2 \, \text{m/s}
\]
Final Answer for (ii):
\[
\boxed{11.2 \, \text{m/s}}
\]
---
Final Answers:
\[
\boxed{-3.2 \, \text{m/s}^2 \quad \text{and} \quad 11.2 \, \text{m/s}}
\]
Parent Tip: Review the logic above to help your child master the concept of speed graph worksheet.
