03. Equation of Motion
Motion in One Dimensions

141726 A metro train starts from rest and in \(5 \mathrm{~s}\) achieves speed of \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141727 A balloon rises from rest with a constant acceleration of \(g / 8\). A stone is released from it when it has risen to a height \(h\). The time taken by the stone to reach the ground is

1 \(4 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(2 \sqrt{\frac{h}{g}}\)
3 \(\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\sqrt{\frac{g}{h}}\)
Motion in One Dimensions

141729 The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^{2}\) and \(y=10 t\) respectively, where \(x\) and \(y\) are in metres and \(t\) in seconds. The acceleration of the particle at \(t=2 s\) is

1 0
2 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-8 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141730 A body kept on a smooth inclined plane having inclination 1 in s will remain stationary relative to inclined plane if the body is given a horizontal acceleration equal to

1 \(\frac{g}{\sqrt{s^{2}-1}}\)
2 \(\frac{g s}{\sqrt{s^{2}-1}}\)
3 \(\frac{\mathrm{g} \sqrt{\mathrm{s}^{2}-1}}{\mathrm{~s}}\)
4 \(g \sqrt{s^{2}-1}\)
Motion in One Dimensions

141731 A particle of mass \(m\) is at \(x=0\) with velocity \(v=\) \(u\) in the \(x\)-direction at \(t=0\), It is subjected to a friction force \(-b v\), where \(b\) is a positive constant.
The position of the particle at \(t \rightarrow \infty\) is

1 \(\mathrm{mu} / \mathrm{b}\)
2 \(\mathrm{u} / \mathrm{mb}\)
3 \(2 \mathrm{mu} / \mathrm{b}\)
4 \(\mathrm{mu} / 2 \mathrm{~b}\)
Motion in One Dimensions

141726 A metro train starts from rest and in \(5 \mathrm{~s}\) achieves speed of \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141727 A balloon rises from rest with a constant acceleration of \(g / 8\). A stone is released from it when it has risen to a height \(h\). The time taken by the stone to reach the ground is

1 \(4 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(2 \sqrt{\frac{h}{g}}\)
3 \(\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\sqrt{\frac{g}{h}}\)
Motion in One Dimensions

141729 The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^{2}\) and \(y=10 t\) respectively, where \(x\) and \(y\) are in metres and \(t\) in seconds. The acceleration of the particle at \(t=2 s\) is

1 0
2 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-8 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141730 A body kept on a smooth inclined plane having inclination 1 in s will remain stationary relative to inclined plane if the body is given a horizontal acceleration equal to

1 \(\frac{g}{\sqrt{s^{2}-1}}\)
2 \(\frac{g s}{\sqrt{s^{2}-1}}\)
3 \(\frac{\mathrm{g} \sqrt{\mathrm{s}^{2}-1}}{\mathrm{~s}}\)
4 \(g \sqrt{s^{2}-1}\)
Motion in One Dimensions

141731 A particle of mass \(m\) is at \(x=0\) with velocity \(v=\) \(u\) in the \(x\)-direction at \(t=0\), It is subjected to a friction force \(-b v\), where \(b\) is a positive constant.
The position of the particle at \(t \rightarrow \infty\) is

1 \(\mathrm{mu} / \mathrm{b}\)
2 \(\mathrm{u} / \mathrm{mb}\)
3 \(2 \mathrm{mu} / \mathrm{b}\)
4 \(\mathrm{mu} / 2 \mathrm{~b}\)
Motion in One Dimensions

141726 A metro train starts from rest and in \(5 \mathrm{~s}\) achieves speed of \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141727 A balloon rises from rest with a constant acceleration of \(g / 8\). A stone is released from it when it has risen to a height \(h\). The time taken by the stone to reach the ground is

1 \(4 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(2 \sqrt{\frac{h}{g}}\)
3 \(\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\sqrt{\frac{g}{h}}\)
Motion in One Dimensions

141729 The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^{2}\) and \(y=10 t\) respectively, where \(x\) and \(y\) are in metres and \(t\) in seconds. The acceleration of the particle at \(t=2 s\) is

1 0
2 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-8 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141730 A body kept on a smooth inclined plane having inclination 1 in s will remain stationary relative to inclined plane if the body is given a horizontal acceleration equal to

1 \(\frac{g}{\sqrt{s^{2}-1}}\)
2 \(\frac{g s}{\sqrt{s^{2}-1}}\)
3 \(\frac{\mathrm{g} \sqrt{\mathrm{s}^{2}-1}}{\mathrm{~s}}\)
4 \(g \sqrt{s^{2}-1}\)
Motion in One Dimensions

141731 A particle of mass \(m\) is at \(x=0\) with velocity \(v=\) \(u\) in the \(x\)-direction at \(t=0\), It is subjected to a friction force \(-b v\), where \(b\) is a positive constant.
The position of the particle at \(t \rightarrow \infty\) is

1 \(\mathrm{mu} / \mathrm{b}\)
2 \(\mathrm{u} / \mathrm{mb}\)
3 \(2 \mathrm{mu} / \mathrm{b}\)
4 \(\mathrm{mu} / 2 \mathrm{~b}\)
Motion in One Dimensions

141726 A metro train starts from rest and in \(5 \mathrm{~s}\) achieves speed of \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141727 A balloon rises from rest with a constant acceleration of \(g / 8\). A stone is released from it when it has risen to a height \(h\). The time taken by the stone to reach the ground is

1 \(4 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(2 \sqrt{\frac{h}{g}}\)
3 \(\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\sqrt{\frac{g}{h}}\)
Motion in One Dimensions

141729 The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^{2}\) and \(y=10 t\) respectively, where \(x\) and \(y\) are in metres and \(t\) in seconds. The acceleration of the particle at \(t=2 s\) is

1 0
2 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-8 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141730 A body kept on a smooth inclined plane having inclination 1 in s will remain stationary relative to inclined plane if the body is given a horizontal acceleration equal to

1 \(\frac{g}{\sqrt{s^{2}-1}}\)
2 \(\frac{g s}{\sqrt{s^{2}-1}}\)
3 \(\frac{\mathrm{g} \sqrt{\mathrm{s}^{2}-1}}{\mathrm{~s}}\)
4 \(g \sqrt{s^{2}-1}\)
Motion in One Dimensions

141731 A particle of mass \(m\) is at \(x=0\) with velocity \(v=\) \(u\) in the \(x\)-direction at \(t=0\), It is subjected to a friction force \(-b v\), where \(b\) is a positive constant.
The position of the particle at \(t \rightarrow \infty\) is

1 \(\mathrm{mu} / \mathrm{b}\)
2 \(\mathrm{u} / \mathrm{mb}\)
3 \(2 \mathrm{mu} / \mathrm{b}\)
4 \(\mathrm{mu} / 2 \mathrm{~b}\)
Motion in One Dimensions

141726 A metro train starts from rest and in \(5 \mathrm{~s}\) achieves speed of \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141727 A balloon rises from rest with a constant acceleration of \(g / 8\). A stone is released from it when it has risen to a height \(h\). The time taken by the stone to reach the ground is

1 \(4 \sqrt{\frac{\mathrm{h}}{\mathrm{g}}}\)
2 \(2 \sqrt{\frac{h}{g}}\)
3 \(\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}\)
4 \(\sqrt{\frac{g}{h}}\)
Motion in One Dimensions

141729 The \(x\) and \(y\) coordinates of the particle at any time are \(x=5 t-2 t^{2}\) and \(y=10 t\) respectively, where \(x\) and \(y\) are in metres and \(t\) in seconds. The acceleration of the particle at \(t=2 s\) is

1 0
2 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-4 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-8 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141730 A body kept on a smooth inclined plane having inclination 1 in s will remain stationary relative to inclined plane if the body is given a horizontal acceleration equal to

1 \(\frac{g}{\sqrt{s^{2}-1}}\)
2 \(\frac{g s}{\sqrt{s^{2}-1}}\)
3 \(\frac{\mathrm{g} \sqrt{\mathrm{s}^{2}-1}}{\mathrm{~s}}\)
4 \(g \sqrt{s^{2}-1}\)
Motion in One Dimensions

141731 A particle of mass \(m\) is at \(x=0\) with velocity \(v=\) \(u\) in the \(x\)-direction at \(t=0\), It is subjected to a friction force \(-b v\), where \(b\) is a positive constant.
The position of the particle at \(t \rightarrow \infty\) is

1 \(\mathrm{mu} / \mathrm{b}\)
2 \(\mathrm{u} / \mathrm{mb}\)
3 \(2 \mathrm{mu} / \mathrm{b}\)
4 \(\mathrm{mu} / 2 \mathrm{~b}\)