$A$ pendulum bob has a speed of $3 \, m/s$ at its lowest position. The pendulum is $50 \, cm$ long. The speed of the bob, when the string makes an angle of $60^{\circ}$ to the vertical, will be $....... \, m/s$ $(g = 10 \, m/s^2)$.

$A$ bead of mass $\frac{1}{2} \, kg$ starts from rest from point $A$ to move in a vertical plane along a smooth fixed quarter ring of radius $5 \, m$,under the action of a constant horizontal force $F = 5 \, N$ as shown. The speed of the bead as it reaches point $B$ is ................ $m/s$. [Take $g = 10 \, m/s^2$]

$A$ bob of a pendulum of length $0.5 \ m$ has a speed of $6 \ ms^{-1}$ at its lowest point. Find the speed of the bob when the string of the pendulum makes $60^{\circ}$ with the vertical. (Take $g=10 \ ms^{-2}$)

$A$ body of mass $6 \,kg$ is acted upon by a force which causes a displacement in it given by $x = \frac{t^2}{4} \,m$, where $t$ is the time in seconds. The work done by the force in $2 \,seconds$ is: (in $\,J$)

Brakes stop a train in a distance $x$. If the braking force is reduced to one-fourth of its original value,what distance will the train travel before coming to a stop?

The displacement-time graph of a particle moving in a straight line is as shown in the figure. Select the correct alternative.