A particle starts with an initial velocity of $10.0 \mathrm{~ms}^{-1}$ along $x$-direction and accelerates uniformly at the rate of $2.0 \mathrm{~ms}^{-2}$. The time taken by the particle to reach the velocity of $60.0 \mathrm{~ms}^{-1}$ is __________.

<p>To find the time taken by the particle to reach the velocity of $60.0 \mathrm{~ms}^{-1}$, we can use the formula:</p> <p>$v = u + at$</p> <p>Where: $v$ is the final velocity, $u$ is the initial velocity, $a$ is the acceleration, and $t$ is the time taken.</p> <p>Plugging in the given values:</p> <p>$60.0 \mathrm{~ms}^{-1} = 10.0 \mathrm{~ms}^{-1} + 2.0 \mathrm{~ms}^{-2} \cdot t$</p> <p>Solve for $t$:</p> <p>$50.0 \mathrm{~ms}^{-1} = 2.0 \mathrm{~ms}^{-2} \cdot t$</p> <p>$t = \frac{50.0 \mathrm{~ms}^{-1}}{2.0 \mathrm{~ms}^{-2}} = 25 \mathrm{s}$</p> <p>So, the time taken by the particle to reach the velocity of $60.0 \mathrm{~ms}^{-1}$ is 25 seconds.</p>