$A$ particle of mass $m$ is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$-direction. Its speed $v(t)$ is depicted by which of the following curves?

$A$ force vector applied on a mass is represented as $\vec F = 6\hat i - 8\hat j + 10\hat k$ and accelerates the body with $1\;m/s^2$. What will be the mass of the body in $kg$?

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 $20 \ N$?

$A$ body of mass $5 \; kg$ is acted upon by two perpendicular forces $8 \; N$ and $6 \; N$. Find the magnitude and direction of the acceleration of the body.

An object of mass $2 \, kg$ at rest at the origin starts moving under the action of a force $\vec{F} = (3t^2 \hat{i} + 4 \hat{j}) \, N$. The velocity of the object at $t = 2 \, s$ will be ............. $m/s$.

$A$ particle of mass $m$ is moving in a straight line with momentum $p$. Starting at time $t = 0$,a force $F = kt$ acts in the same direction on the moving particle during time interval $T$ so that its momentum changes from $p$ to $3p$. Here $k$ is a constant. The value of $T$ is