00. Distance and Displacement
Motion in One Dimensions

141230 The position of a particle as a function of time \(t\), is given by \(x(t)=a t+b t^{2}-c t^{3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

1 \(a+\frac{b^{2}}{2 c}\)
2 \(a+\frac{b^{2}}{4 c}\)
3 \(a+\frac{b^{2}}{3 c}\)
4 \(a+\frac{b^{2}}{c}\)
Motion in One Dimensions

141232 A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(\mathrm{X}\)-axis. Identify all figures that correctly represent the motion qualitatively. \((a=\) acceleration, \(v=\) velocity,
\(x=\) displacement, \(t=\) time \()\)

1 \((\mathrm{A})\)
2 (B), (C)
3 \((\mathrm{A}),(\mathrm{B}),(\mathrm{C})\)
4 (A), (B), (D)
Motion in One Dimensions

141233 A particle starts from the origin at time \(t=0\) and moves along the positive \(\mathrm{X}\)-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(\mathrm{t}=5 \mathrm{~s}\) ?
original image

1 \(6 \mathrm{~m}\)
2 \(3 \mathrm{~m}\)
3 \(10 \mathrm{~m}\)
4 \(9 \mathrm{~m}\)
Motion in One Dimensions

141234 A person travelling in a straight line moves with a constant velocity \(v_{1}\) for certain distance ' \(x\) ' and with a constant velocity \(v_{2}\) for next equal distance. The average velocity \(v\) is given by the relation

1 \(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
2 \(\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
3 \(\frac{\mathrm{v}}{2}=\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\)
4 \(\mathrm{v}=\sqrt{\mathrm{v}_{1} \mathrm{v}_{2}}\)
Motion in One Dimensions

141235 A ball is thrown in horizontal direction from a height of \(80 \mathrm{~m}\) with initial speed \(v_{0}\). The ball hits the ground with speed \(3 v_{0}\). The magnitude of \(v_{0}\) is \(\left(\right.\) Let \(\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(18 \mathrm{~m} / \mathrm{s}\)
4 \(26 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141230 The position of a particle as a function of time \(t\), is given by \(x(t)=a t+b t^{2}-c t^{3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

1 \(a+\frac{b^{2}}{2 c}\)
2 \(a+\frac{b^{2}}{4 c}\)
3 \(a+\frac{b^{2}}{3 c}\)
4 \(a+\frac{b^{2}}{c}\)
Motion in One Dimensions

141232 A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(\mathrm{X}\)-axis. Identify all figures that correctly represent the motion qualitatively. \((a=\) acceleration, \(v=\) velocity,
\(x=\) displacement, \(t=\) time \()\)

1 \((\mathrm{A})\)
2 (B), (C)
3 \((\mathrm{A}),(\mathrm{B}),(\mathrm{C})\)
4 (A), (B), (D)
Motion in One Dimensions

141233 A particle starts from the origin at time \(t=0\) and moves along the positive \(\mathrm{X}\)-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(\mathrm{t}=5 \mathrm{~s}\) ?
original image

1 \(6 \mathrm{~m}\)
2 \(3 \mathrm{~m}\)
3 \(10 \mathrm{~m}\)
4 \(9 \mathrm{~m}\)
Motion in One Dimensions

141234 A person travelling in a straight line moves with a constant velocity \(v_{1}\) for certain distance ' \(x\) ' and with a constant velocity \(v_{2}\) for next equal distance. The average velocity \(v\) is given by the relation

1 \(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
2 \(\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
3 \(\frac{\mathrm{v}}{2}=\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\)
4 \(\mathrm{v}=\sqrt{\mathrm{v}_{1} \mathrm{v}_{2}}\)
Motion in One Dimensions

141235 A ball is thrown in horizontal direction from a height of \(80 \mathrm{~m}\) with initial speed \(v_{0}\). The ball hits the ground with speed \(3 v_{0}\). The magnitude of \(v_{0}\) is \(\left(\right.\) Let \(\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(18 \mathrm{~m} / \mathrm{s}\)
4 \(26 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141230 The position of a particle as a function of time \(t\), is given by \(x(t)=a t+b t^{2}-c t^{3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

1 \(a+\frac{b^{2}}{2 c}\)
2 \(a+\frac{b^{2}}{4 c}\)
3 \(a+\frac{b^{2}}{3 c}\)
4 \(a+\frac{b^{2}}{c}\)
Motion in One Dimensions

141232 A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(\mathrm{X}\)-axis. Identify all figures that correctly represent the motion qualitatively. \((a=\) acceleration, \(v=\) velocity,
\(x=\) displacement, \(t=\) time \()\)

1 \((\mathrm{A})\)
2 (B), (C)
3 \((\mathrm{A}),(\mathrm{B}),(\mathrm{C})\)
4 (A), (B), (D)
Motion in One Dimensions

141233 A particle starts from the origin at time \(t=0\) and moves along the positive \(\mathrm{X}\)-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(\mathrm{t}=5 \mathrm{~s}\) ?
original image

1 \(6 \mathrm{~m}\)
2 \(3 \mathrm{~m}\)
3 \(10 \mathrm{~m}\)
4 \(9 \mathrm{~m}\)
Motion in One Dimensions

141234 A person travelling in a straight line moves with a constant velocity \(v_{1}\) for certain distance ' \(x\) ' and with a constant velocity \(v_{2}\) for next equal distance. The average velocity \(v\) is given by the relation

1 \(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
2 \(\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
3 \(\frac{\mathrm{v}}{2}=\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\)
4 \(\mathrm{v}=\sqrt{\mathrm{v}_{1} \mathrm{v}_{2}}\)
Motion in One Dimensions

141235 A ball is thrown in horizontal direction from a height of \(80 \mathrm{~m}\) with initial speed \(v_{0}\). The ball hits the ground with speed \(3 v_{0}\). The magnitude of \(v_{0}\) is \(\left(\right.\) Let \(\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(18 \mathrm{~m} / \mathrm{s}\)
4 \(26 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141230 The position of a particle as a function of time \(t\), is given by \(x(t)=a t+b t^{2}-c t^{3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

1 \(a+\frac{b^{2}}{2 c}\)
2 \(a+\frac{b^{2}}{4 c}\)
3 \(a+\frac{b^{2}}{3 c}\)
4 \(a+\frac{b^{2}}{c}\)
Motion in One Dimensions

141232 A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(\mathrm{X}\)-axis. Identify all figures that correctly represent the motion qualitatively. \((a=\) acceleration, \(v=\) velocity,
\(x=\) displacement, \(t=\) time \()\)

1 \((\mathrm{A})\)
2 (B), (C)
3 \((\mathrm{A}),(\mathrm{B}),(\mathrm{C})\)
4 (A), (B), (D)
Motion in One Dimensions

141233 A particle starts from the origin at time \(t=0\) and moves along the positive \(\mathrm{X}\)-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(\mathrm{t}=5 \mathrm{~s}\) ?
original image

1 \(6 \mathrm{~m}\)
2 \(3 \mathrm{~m}\)
3 \(10 \mathrm{~m}\)
4 \(9 \mathrm{~m}\)
Motion in One Dimensions

141234 A person travelling in a straight line moves with a constant velocity \(v_{1}\) for certain distance ' \(x\) ' and with a constant velocity \(v_{2}\) for next equal distance. The average velocity \(v\) is given by the relation

1 \(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
2 \(\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
3 \(\frac{\mathrm{v}}{2}=\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\)
4 \(\mathrm{v}=\sqrt{\mathrm{v}_{1} \mathrm{v}_{2}}\)
Motion in One Dimensions

141235 A ball is thrown in horizontal direction from a height of \(80 \mathrm{~m}\) with initial speed \(v_{0}\). The ball hits the ground with speed \(3 v_{0}\). The magnitude of \(v_{0}\) is \(\left(\right.\) Let \(\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(18 \mathrm{~m} / \mathrm{s}\)
4 \(26 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141230 The position of a particle as a function of time \(t\), is given by \(x(t)=a t+b t^{2}-c t^{3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

1 \(a+\frac{b^{2}}{2 c}\)
2 \(a+\frac{b^{2}}{4 c}\)
3 \(a+\frac{b^{2}}{3 c}\)
4 \(a+\frac{b^{2}}{c}\)
Motion in One Dimensions

141232 A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(\mathrm{X}\)-axis. Identify all figures that correctly represent the motion qualitatively. \((a=\) acceleration, \(v=\) velocity,
\(x=\) displacement, \(t=\) time \()\)

1 \((\mathrm{A})\)
2 (B), (C)
3 \((\mathrm{A}),(\mathrm{B}),(\mathrm{C})\)
4 (A), (B), (D)
Motion in One Dimensions

141233 A particle starts from the origin at time \(t=0\) and moves along the positive \(\mathrm{X}\)-axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(\mathrm{t}=5 \mathrm{~s}\) ?
original image

1 \(6 \mathrm{~m}\)
2 \(3 \mathrm{~m}\)
3 \(10 \mathrm{~m}\)
4 \(9 \mathrm{~m}\)
Motion in One Dimensions

141234 A person travelling in a straight line moves with a constant velocity \(v_{1}\) for certain distance ' \(x\) ' and with a constant velocity \(v_{2}\) for next equal distance. The average velocity \(v\) is given by the relation

1 \(\frac{1}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
2 \(\frac{2}{\mathrm{v}}=\frac{1}{\mathrm{v}_{1}}+\frac{1}{\mathrm{v}_{2}}\)
3 \(\frac{\mathrm{v}}{2}=\frac{\mathrm{v}_{1}+\mathrm{v}_{2}}{2}\)
4 \(\mathrm{v}=\sqrt{\mathrm{v}_{1} \mathrm{v}_{2}}\)
Motion in One Dimensions

141235 A ball is thrown in horizontal direction from a height of \(80 \mathrm{~m}\) with initial speed \(v_{0}\). The ball hits the ground with speed \(3 v_{0}\). The magnitude of \(v_{0}\) is \(\left(\right.\) Let \(\left.g=9.8 \mathrm{~m} / \mathrm{s}^{2}\right)\)

1 \(10 \mathrm{~m} / \mathrm{s}\)
2 \(14 \mathrm{~m} / \mathrm{s}\)
3 \(18 \mathrm{~m} / \mathrm{s}\)
4 \(26 \mathrm{~m} / \mathrm{s}\)