Question

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

• A. a constant
• B. proportional to $t^2$
• C. inversely proportional to $t$
• D. proportional to $t$

Answer 1

Answer: (D)

proportional to $t$

Given, $p=a+{bt}^2$
$\frac{dp}{dt}=2bt$
$\because F=\frac{dp}{dt}$
$\therefore F=2bt$
or $F\propto t$