A river has a steady speed of $v$. A man swims upstream at a distance of $d$ and swims back to the starting point in total time $t$. The man can swim at a speed of $2 v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same length of swim, then $\frac{t}{t_0}$ is

A body starts from the rest and acquires a velocity of $10 \mathrm{~m} / \mathrm{s}$ in 2s. What is the acceleration of the body and the distance travelled?

A bullet fired into a target losses one-third of its velocity after travelling a distance $x$ metre into the target. If the bullet comes to rest by travelling a further distance $x^{\prime}$, then the ratio $\frac{x^{\prime}}{x}$ is

A ball is thrown straight upward from ground with a speed of $20 \mathrm{~m} / \mathrm{s}$. The ball was caught on its way down at a point 5 m above the ground. The time taken by the ball during entire trip is (assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ )