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B X A A car starts at Point A at t = 0s with a speed vo = 16 km/h. Its speed increases at a constant rate to Point C, where its velocity is vc = 110 km/h. The curved portion has a radius, r = 111 m, and the distance between Point B and Point C is, x = 138 m. Determine the car's speed at Point B. Use one decimal place in your answer and report your answer in km/h.

B X A A car starts at Point A at t = 0s with a speed vo = 16 km/h. Its speed increases at a constant rate to Point C, where its velocity is vc = 110 km/h. The curved portion has a radius, r = 111 m, and the distance between Point B and Point C is, x = 138 m. Determine the car's speed at Point B. Use one decimal place in your answer and report your answer in km/h.

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### Problem Statement: A car starts at **Point A** at time \( t = 0 \) seconds with an initial speed \( v_0 = 16 \) km/h. Its speed increases at a constant rate until it reaches **Point C**, where its velocity is \( v_C = 110 \) km/h. The curved portion of the road has a radius \( r = 111 \) meters, and the distance between **Point B** and **Point C** is \( x = 138 \) meters. ### Task: Determine the car's speed at **Point B**. Use one decimal place in your answer and report your result in km/h. **Hint:** Make sure to convert all quantities to the correct units before performing calculations! ### Explanation of Diagram: The provided diagram shows a road with three key points, **A**, **B**, and **C**, along the path a car takes. - **Point A** is the starting point on a curved section of the road. - **Point B** is the endpoint of the curved section and the beginning of the straight section. - **Point C** is the endpoint of the straight section. The radius of the curved portion of the road is labeled as \( r = 111 \) meters. The straight distance between **Point B** and **Point C** is labeled as \( x = 138 \) meters. ### Approach: 1. **Analyze the Kinematics:** - Identify the initial velocity at Point A ( \( v_0 = 16 \) km/h) and the final velocity at Point C ( \( v_C = 110 \) km/h). - Assume the acceleration is constant. 2. **Determine Unit Consistency:** - Ensure all measurements are in compatible units for proper calculation. 3. **Calculate the Speed at Point B:** - Using kinematic equations or principles of dynamics, solve for the velocity at Point B. The solution will involve applying the appropriate physics principles to determine the car's speed at Point B, ensuring each step follows logically from the provided data and established kinematics rules.
Transcribed Image Text:### Problem Statement: A car starts at **Point A** at time \( t = 0 \) seconds with an initial speed \( v_0 = 16 \) km/h. Its speed increases at a constant rate until it reaches **Point C**, where its velocity is \( v_C = 110 \) km/h. The curved portion of the road has a radius \( r = 111 \) meters, and the distance between **Point B** and **Point C** is \( x = 138 \) meters. ### Task: Determine the car's speed at **Point B**. Use one decimal place in your answer and report your result in km/h. **Hint:** Make sure to convert all quantities to the correct units before performing calculations! ### Explanation of Diagram: The provided diagram shows a road with three key points, **A**, **B**, and **C**, along the path a car takes. - **Point A** is the starting point on a curved section of the road. - **Point B** is the endpoint of the curved section and the beginning of the straight section. - **Point C** is the endpoint of the straight section. The radius of the curved portion of the road is labeled as \( r = 111 \) meters. The straight distance between **Point B** and **Point C** is labeled as \( x = 138 \) meters. ### Approach: 1. **Analyze the Kinematics:** - Identify the initial velocity at Point A ( \( v_0 = 16 \) km/h) and the final velocity at Point C ( \( v_C = 110 \) km/h). - Assume the acceleration is constant. 2. **Determine Unit Consistency:** - Ensure all measurements are in compatible units for proper calculation. 3. **Calculate the Speed at Point B:** - Using kinematic equations or principles of dynamics, solve for the velocity at Point B. The solution will involve applying the appropriate physics principles to determine the car's speed at Point B, ensuring each step follows logically from the provided data and established kinematics rules.
For the figure of Question 1 and using the following values: - \(r = 150 \, \text{m}\) - \(x = 100 \, \text{m}\) - \(v_A = 0 \, \text{km/hr}\) - \(a_t = 1.15 \, \text{m/s}^2\) Calculate the magnitude of the car's **acceleration**, \(a\), when \(t = 10 \, \text{s}\). Use **two decimal places** in your answer and report your answer in \(\text{m/s}^2\). **Hint:** Where is the car located at this time?
Transcribed Image Text:For the figure of Question 1 and using the following values: - \(r = 150 \, \text{m}\) - \(x = 100 \, \text{m}\) - \(v_A = 0 \, \text{km/hr}\) - \(a_t = 1.15 \, \text{m/s}^2\) Calculate the magnitude of the car's **acceleration**, \(a\), when \(t = 10 \, \text{s}\). Use **two decimal places** in your answer and report your answer in \(\text{m/s}^2\). **Hint:** Where is the car located at this time?
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