A particle is moving with acceleration $\overrightarrow{a}=(\hat{i}+\hat{j}){\text{m/s}}^2$ and its initial velocity (at $t=0$) is ${\overrightarrow{v}}_0=(\hat{i}-\hat{j})\text{m/s}$. Rate of change of speed of the particle at $t=0$ is

Q. A particle is moving on a circular path of radius $1m$ and its speed is changing as $v=2t$. The magnitude of the acceleration of particle at time $t=1s$ is

Q. A particle is moving on a circular path of 10 m radius. At any instant of time, its speed is 5 m/s and the speed is increasing at a rate of $2m/s^2$. The magnitude of net acceleration at this instant is:

Q. A particle moving along positive $x-$axis with a speed $5{\text{ms}}^{–1}$ suddenly changes its direction along the positive $y-$axis with the same speed. The change in velocity $\Delta \overrightarrow{v}$ of the particle is -

Q. A particle is revolving in a circular path having radius $‘r^{\prime }=1m$ at a speed of $2m/s$. It is increasing its speed at the rate of $3m/s^2$. The magnitude of total acceleration of the particle at that instant is

Q. A particle is constrained to move in a circle of radius $300\text{cm}$. Its linear speed increases with time as $v=2t$, where $t$ is in second and $v$ is in $\text{m/s}$. The acceleration of the particle at $t=3\text{s}$ is