A car moves from X to Y with a uniform speed ${v_u}$ and returns to Y with a uniform speed ${v_d}$. The average speed for this round trip is

A boat travels 50 km east, then 120 km north and finally it comes back to the starting point through the shortest distance. The total time of journey is 3 h. What is the average speed, in ${\rm{km}}{{\rm{h}}^{ - 1}},$, over the entire trip?

A projectile is launched at an angle $heta$ with the horizontal with an initial speed $u$. If the horizontal range is $R$ and the maximum height reached is $H$, what is the relationship between $R$, $H$, and $heta$?

Essential characteristic of equilibrium is

If the velocity of a particle is $\left( {10 + 2{t^2}} \right)m/s$, then the average acceleration of the particle between 2s and 5s is

A particle starts from rest and moves along a straight line with an acceleration given by $a = 6t - 4$, where $a$ is in $m/s^2$ and $t$ is in seconds. At what time is the velocity of the particle zero after the start of motion?

A particle covers half of its total distance with speed ${v_1}$ and the rest half distance with speed ${v_2}$. Its average speed during the complete journey is

A car travels 20 m in 2 seconds and 40 m in the next 4 seconds. What is its average acceleration?

The x and y coordinates of a particles at any time t are given by $x = 7t + 4{t^2}\,\,and\,\,y = 5t,$, where x and y are in metre and t in second. The acceleration of particle at t=5s is

A particle starts from rest and moves with uniform acceleration. After covering a distance $d$, its velocity becomes $v$. How much further will it travel before its velocity doubles to $2v$?

A man is 45 m behind the bus, when the bus starts accelerating from rest with acceleration $2.5\;{\rm{m}}{{\rm{s}}^{ - 2}}.$. With what minimum velocity should the man start running to catch the bus?