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4 m M (302) N-m %3D F = 15t N. If the rod of negligible mass is subjected to a couple moment of M=29t2 N;M where t is the time in seconds, and the engine of the car supplies a braking force F= 15t N to the wheels, determine the speed of the car at t= 8s. The car at t=0s a a speed of 7 m/s. The total mass of the car and the driver is 158 kg. Neglect the size of the car.

4 m M (302) N-m %3D F = 15t N. If the rod of negligible mass is subjected to a couple moment of M=29t2 N;M where t is the time in seconds, and the engine of the car supplies a braking force F= 15t N to the wheels, determine the speed of the car at t= 8s. The car at t=0s a a speed of 7 m/s. The total mass of the car and the driver is 158 kg. Neglect the size of the car.

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The image depicts a car attached to a rod of negligible mass, which is subjected to a couple moment defined by \( M = 29t^2 \, \text{N} \cdot \text{m} \), where \( t \) is the time in seconds. The engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels. The scenario requires determining the speed of the car at \( t = 8 \) seconds, given that the car initially has a speed of \( 7 \, \text{m/s} \) at \( t = 0 \). The total mass of the car and the driver is \( 158 \, \text{kg} \), and the size of the car is neglected. ### Diagram Explanation: - **Components:** - A horizontal rod, \( 4 \, \text{m} \) in length, connected to a pivot point. - A car attached to the end of the rod. - A driver seated inside the car. - Arrows depicting the couple moment \( M \) and braking force \( F \). - **Labels:** - \( M = (30t^2) \, \text{N} \cdot \text{m} \) indicating the couple moment applied to the rod. - \( F = 15t \, \text{N} \) representing the braking force applied by the engine. ### Problem Statement: "If the rod of negligible mass is subjected to a couple moment of \( M = 29t^2 \, \text{N} \cdot \text{m} \) where \( t \) is the time in seconds, and the engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels, determine the speed of the car at \( t = 8 \) seconds. The car at \( t = 0 \) has a speed of \( 7 \, \text{m/s} \). The total mass of the car and the driver is \( 158 \, \text{kg} \). Neglect the size of the car."
Transcribed Image Text:The image depicts a car attached to a rod of negligible mass, which is subjected to a couple moment defined by \( M = 29t^2 \, \text{N} \cdot \text{m} \), where \( t \) is the time in seconds. The engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels. The scenario requires determining the speed of the car at \( t = 8 \) seconds, given that the car initially has a speed of \( 7 \, \text{m/s} \) at \( t = 0 \). The total mass of the car and the driver is \( 158 \, \text{kg} \), and the size of the car is neglected. ### Diagram Explanation: - **Components:** - A horizontal rod, \( 4 \, \text{m} \) in length, connected to a pivot point. - A car attached to the end of the rod. - A driver seated inside the car. - Arrows depicting the couple moment \( M \) and braking force \( F \). - **Labels:** - \( M = (30t^2) \, \text{N} \cdot \text{m} \) indicating the couple moment applied to the rod. - \( F = 15t \, \text{N} \) representing the braking force applied by the engine. ### Problem Statement: "If the rod of negligible mass is subjected to a couple moment of \( M = 29t^2 \, \text{N} \cdot \text{m} \) where \( t \) is the time in seconds, and the engine of the car supplies a braking force \( F = 15t \, \text{N} \) to the wheels, determine the speed of the car at \( t = 8 \) seconds. The car at \( t = 0 \) has a speed of \( 7 \, \text{m/s} \). The total mass of the car and the driver is \( 158 \, \text{kg} \). Neglect the size of the car."
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