Q. If a(acceleration) = x², then find v(velocity) when x is 2m. Given at x = 0 and body is at rest.
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Given accl. = x^2
then velo. = integration of x^2 = x^3/3 + c
putting value of x= 0 and as velocity is rest so it is zero
then 0 = 0 + c => c = 0
then velocity = x^3/3
Now velocity when x = 2 is
velocity = 2^3/ 3 = 8/3 = 3.67m/sec
So your answer is 3.67m/s.
then velo. = integration of x^2 = x^3/3 + c
putting value of x= 0 and as velocity is rest so it is zero
then 0 = 0 + c => c = 0
then velocity = x^3/3
Now velocity when x = 2 is
velocity = 2^3/ 3 = 8/3 = 3.67m/sec
So your answer is 3.67m/s.
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