prove that half mv sqaure
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Half mv sq. is the formula of kinetic energy (K.E.)
suppose a stationary object of mass m moves because of an applied force. let u be its initial velocity (Here u=0 ) . Let the applied force be F. This generates an acceleration a. in the object, and, after time t, the velocity of the object becomes equal to v. The displacement during this time is s. The work done on the object,
W=F×s
according to Newton's 2nd law of motion,
F=ma .... (1) Similarly, using Newton's 2nd equation of motion.
s=ut+1/2at sq....However, as initial velocity is 0, u=0.
s=0+1/2at sq. .... (2)
therefore,W=ma× 1/2at sq. ..... using equation (1) and (2)
W= 1/2m(at) sq. ......(3)
Using Newtons 1st equation of motion.......
v= u + at
v= 0+ at
:= at
v sq.= (at) sq. .....(4)
W=1/2 mv sq. ....... using equation (3) and (4)
The Kinetic energy gained by an object is the amount of work done on the object.
therefore, K.E. = W
K.E. = 1/2 mv sq.
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suppose a stationary object of mass m moves because of an applied force. let u be its initial velocity (Here u=0 ) . Let the applied force be F. This generates an acceleration a. in the object, and, after time t, the velocity of the object becomes equal to v. The displacement during this time is s. The work done on the object,
W=F×s
according to Newton's 2nd law of motion,
F=ma .... (1) Similarly, using Newton's 2nd equation of motion.
s=ut+1/2at sq....However, as initial velocity is 0, u=0.
s=0+1/2at sq. .... (2)
therefore,W=ma× 1/2at sq. ..... using equation (1) and (2)
W= 1/2m(at) sq. ......(3)
Using Newtons 1st equation of motion.......
v= u + at
v= 0+ at
:= at
v sq.= (at) sq. .....(4)
W=1/2 mv sq. ....... using equation (3) and (4)
The Kinetic energy gained by an object is the amount of work done on the object.
therefore, K.E. = W
K.E. = 1/2 mv sq.
*********************
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