The linear momentum p of a body moving in one dimension varies with time t according to the equation p = a + bt2, where a and b are positive constant. The net force acting on the body is

Question

The linear momentum p of a body moving in one dimension varies with time t according to the equation p = a + bt2, where a and b are positive constant. The net force acting on the body is (A) a constant (B) proportional to t2 (C) inversely proportional to t (D) proportional to t

Tardigrade Admin · Accepted Answer

Given, P = a + bt2 (dP/dt) = 2bt ∵ F = (dP/dt) ∴ F = 2bt or F propto t

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

a constant

proportional to $t^{2}$

inversely proportional to $t$

proportional to $t$

Given, $P = a + b t^{2}$
$\frac{d P}{d t} = 2 b t$
$∵ F = \frac{d P}{d t}$
$∴ F = 2 b t$
or $F \propto t$

Q. The linear momentum p of a body moving in one dimension varies with time t according to the equation p=a+bt2, where a and b are positive constant. The net force acting on the body is

a constant

proportional to t2

inversely proportional to t

proportional to t

Given, P=a+bt2 dtdP​=2bt ∵F=dtdP​ ∴F=2bt or F∝t

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

proportional to $t^{2}$

inversely proportional to $t$

proportional to $t$

Given, $P = a + b t^{2}$
$\frac{d P}{d t} = 2 b t$
$∵ F = \frac{d P}{d t}$
$∴ F = 2 b t$
or $F \propto t$