$A$ force on an object of mass $100\, g$ is $(10 \hat{i}+5 \hat{j})\ N$. The position of that object at $t= 2\ s$ is $(a \hat{i}+b \hat{j})\, m$ after starting from rest. The value of $\frac{a}{b}$ will be..........

Which physical quantity is represented by the first derivative of linear momentum with respect to time?

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

An object with mass $5 \ kg$ is acted upon by a force,$\vec{F}=(-3 \hat{i}+4 \hat{j}) \ N$. If its initial velocity at $t=0$ is $\vec{v}=(6 \hat{i}-12 \hat{j}) \ ms^{-1}$,the time at which it will just have a velocity along the $y$-axis is: (in $s$)

An object with a mass of $10\, kg$ moves at a constant velocity of $10\, m/s$. $A$ constant force then acts for $4\, s$ on the object and gives it a speed of $2\, m/s$ in the opposite direction. The force acting on the object is ......... $N$.

The driver of a three-wheeler moving with a speed of $36\; km/h$ sees a child standing in the middle of the road and brings his vehicle to rest in $4.0\; s$ just in time to save the child. What is the average retarding force (in $N$) on the vehicle? The mass of the three-wheeler is $400\; kg$ and the mass of the driver is $65\; kg$.