The linear momentum p of a body moving in one | vedclass

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(D) According to Newton's second law of motion,the net force $F$ acting on a body is equal to the rate of change of its linear momentum $p$ with respe

Vedclass · Accepted Answer

Proportional to $t$

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(D) According to Newton's second law of motion,the net force $F$ acting on a body is equal to the rate of change of its linear momentum $p$ with respect to time $t$. Mathematically,$F = \frac{dp}{dt}$. Given the equation for momentum is $p = a + bt^2$. Differentiating this equation with respect to time $t$,we get: $F = \frac{d}{dt}(a + bt^2)$. Since $a$ is a constant,its derivative is $0$. $F = 0 + b(2t) = 2bt$. Since $2$ and $b$ are constants,we can conclude that $F \propto t$. Therefore,the net force acting on the body is proportional to $t$.

The linear momentum $p$ of a body moving in one dimension varies with time according to the equation $p = a + bt^2$,where $a$ and $b$ are positive constants. The net force acting on the body is

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