At any instant,the velocity of a particle of mass $500 \, g$ is $(2t \hat{i} + 3t^2 \hat{j}) \, ms^{-1}$. If the force acting on the particle at $t = 1 \, s$ is $(\hat{i} + x \hat{j}) \, N$,then the value of $x$ will be:

$A$ constant force acts on a body of mass $0.9 \,kg$ at rest for $10 \,s$. If the body moves a distance of $250 \,m$,the magnitude of the force is.........$N$

$A$ body under the action of a force $\vec{F} = 6\hat{i} - 8\hat{j} \text{ N}$ acquires an acceleration of $5 \text{ m s}^{-2}$. The mass of the body is ........ $\text{kg}$.

$A$ particle of mass $2/3 \, kg$ with velocity $v = -15 \, m/s$ at $t = -2 \, s$ is acted upon by a force $F = k - \beta t^2$. Here,$k = 8 \, N$ and $\beta = 2 \, N/s^2$. The motion is one-dimensional. Then,the speed at which the particle acceleration is zero again,is ........... $m/s$.

$A$ force $\vec{F_1}$ of magnitude $4 \ N$ acts on an object of mass $1 \ kg$ at the origin in a direction $30^{\circ}$ above the positive $x$-axis. $A$ second force $\vec{F_2}$ of magnitude $4 \ N$ acts on the same object in the direction of the positive $y$-axis. The magnitude of the acceleration of the object is nearly: (in $m \ s^{-2}$)

$5\, kg$ દળ ધરાવતા એક પદાર્થ પર અચળ બળ $\overrightarrow F = {F_x}\hat i + {F_y}\hat j$ લાગે છે. $t = 0\, s$ સમયે તેનો વેગ $\overrightarrow v = (6\hat i - 2\hat j)\, m/s$ છે અને $t = 10\, s$ સમયે તેનો વેગ $\overrightarrow v = 6\hat j\, m/s$ છે. તો બળ $\overrightarrow F$ શોધો.