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) \( mA \int_{0}^{t_1} e^{-kt} dt \)
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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