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

$A$ constant force $\overrightarrow F = F_x\hat i + F_y\hat j$ acts on a body of mass $5\, kg$. At $t = 0\, s$, its velocity is $\overrightarrow v = (6\hat i - 2\hat j)\, m/s$ and at $t = 10\, s$, its velocity is $\overrightarrow v = 6\hat j\, m/s$. Find the force $\overrightarrow F$.

The velocity of an object of mass $2 \ kg$ is given by $v = (8t \hat{i} + 3t^2 \hat{j}) \ m/s$, where $t$ is time in seconds. What will be the direction of the net force on the object relative to the positive direction of the $X$-axis, at the instant when its magnitude is $20 \ N$?

An army vehicle of mass $1000\, kg$ is moving with a velocity of $10\, m/s$. It is acted upon by a forward force of $1000\, N$ due to the engine and a retarding force of $500\, N$ due to friction. What will be its velocity after $10\, s$ (in $, m/s$)?

The average resisting force that must act on a $5 \,kg$ mass to reduce its speed from $65 \,cm/s$ to $15 \,cm/s$ in $0.2 \,s$ is .......... $N$.

An object of mass $3\,kg$ is at rest. If a force $\vec{F} = (6t^2\hat{i} + 4t\hat{j})\,N$ is applied on the object,then the velocity of the object at $t = 3\,s$ will be