$A$ particle has an initial velocity of $(\hat{i} + \hat{j}) \, m/s$ and an acceleration of $(\hat{i} + \hat{j}) \, m/s^2$. Its speed after $10 \, s$ will be:

The initial position of an object at rest is given by $3 \hat{i}-8 \hat{j}$. It moves with constant acceleration and reaches the position $2 \hat{i}+4 \hat{j}$ after $4 \, s$. What is its acceleration?

$A$ particle is in uniform circular motion. Related to one complete revolution of the particle, which among the statements is incorrect?

Balls $A$ and $B$ are thrown from two points lying on the same horizontal plane separated by a distance of $120\,m$. Which of the following statement$(s)$ is/are correct?

Three particles,located initially on the vertices of an equilateral triangle of side $L$,start moving with a constant speed $v$ towards each other in a cyclic manner,forming spiral loci that converge at the centroid of the triangle. The length of one such spiral locus will be

At a given instant of time, the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is: