A block of mass m is pulled by a rope along a horizontal surface with negligible friction. For time t> 0, the magnitude of the acceleration of the object as a function of time is given by the equation a = Aekt, where A and k are positive constants. Which of the following ex determines the impulse exerted on the block by the rope during the time interval 0
A block of mass m is pulled by a rope along a horizontal surface with negligible friction. For time t> 0, the magnitude of the acceleration of the object as a function of time is given by the equation a = Aekt, where A and k are positive constants. Which of the following ex determines the impulse exerted on the block by the rope during the time interval 0
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![A block of mass \( m \) is pulled by a rope along a horizontal surface with negligible friction. For time \( t > 0 \), the magnitude of the acceleration of the object as a function of time is given by the equation \( a = Ae^{-kt} \), where \( A \) and \( k \) are positive constants. Which of the following expressions determines the impulse exerted on the block by the rope during the time interval \( 0 < t < t_1 \)?
Options:
- (A) \( A \int_{0}^{t_1} e^{-kt} dt \)
- (B) \( mA \frac{d}{dt} [e^{-kt}]_{t_1} \)
- (C) \( A \frac{d}{dt} [e^{-kt}]_{t_1} \)
- (D) \( mA t_1 [e^{-kt}] \)
- (E) \( mA \int_{0}^{t_1} e^{-kt} dt \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37718c2d-4444-454a-bbc0-0a0844d4b623%2Fa57ae476-935c-4d41-96ec-99f3dd106f84%2Fs1h21v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A block of mass \( m \) is pulled by a rope along a horizontal surface with negligible friction. For time \( t > 0 \), the magnitude of the acceleration of the object as a function of time is given by the equation \( a = Ae^{-kt} \), where \( A \) and \( k \) are positive constants. Which of the following expressions determines the impulse exerted on the block by the rope during the time interval \( 0 < t < t_1 \)?
Options:
- (A) \( A \int_{0}^{t_1} e^{-kt} dt \)
- (B) \( mA \frac{d}{dt} [e^{-kt}]_{t_1} \)
- (C) \( A \frac{d}{dt} [e^{-kt}]_{t_1} \)
- (D) \( mA t_1 [e^{-kt}] \)
- (E) \( mA \int_{0}^{t_1} e^{-kt} dt \)
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