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With a given braking system (car or rocketship), the system has to dissipate the Kinetic energy of the object. Kinetic formula for K.E. is 1/2MV2 (that 2 means squared). Therefore, the stopping distance increases linearly with the MASS.

Another way to look at it is the Force required to stop the MASS, which is:

F=M x A, so again as MASS increases the required Force increases Linearly.

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