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Question

Give the relation between acceleration, mass, and force.


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Solution

Step1: Newton's second law

  1. Newton's second law describes the relationship between the three quantities above.
  2. The rate of change of momentum of a body is equal to the force exerted on the body in a given direction, according to Newton's second law of motion.

Step2: Formula used

Consider a body with mass 'm' that moves at velocity 'v'. As a result, the body's momentum 'p' is given by,

p=mv

Step3: Relation between acceleration, mass, and force

We now know that the rate of change in momentum of a body is equal to the force applied to the body thanks to Newton's second law of motion. As a result, the force F equals, F=dpdt=d(mv)dt[Asp=mv]

F=vdmdt+mdvdt...........equtaion(i)

The acceleration 'a'of a body is defined as the rate of change of velocity i.e. dvdt

since mass does not change with time equation (i) can be written as,

F=vdmdt+mdvdtF=v(0)+maF=ma

Hence the required relation between acceleration, mass, and force is given by F=ma


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