00. Distance and Displacement
Motion in One Dimensions

141197 A cyclist traversed half the distance of a linear track with a velocity \(10 \mathrm{~m} / \mathrm{s}\). The remaining part of the track was covered with a velocity \(\vec{v}_{1}\) for half the time and a velocity \(\vec{v}_{2}\) for the other half of the time. If \(\vec{v}_{1}+\vec{v}_{2}=20 \mathrm{~m} / \mathrm{s}\), then the average velocity of the cyclist during the completion of the journey through the track is:

1 \(30 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(15 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141198 A car travels in a straight line along a road. Its distance ' \(x\) ' from a stop sign is given as a function of ' \(t\) ' by the equation \(x(t)=\alpha t+\beta t^{3}\), where \(\alpha=2.0 \mathrm{~m} / \mathrm{s}, \beta=0.01 \mathrm{~m} / \mathrm{s}^{3}\). Calculate the average velocity of the car in the time interval \(t\) \(=2.00 \mathrm{sec}\) to \(4.00 \mathrm{sec}\).

1 \(2.28 \mathrm{~m} / \mathrm{s}\)
2 \(4.94 \mathrm{~m} / \mathrm{s}\)
3 \(3.34 \mathrm{~m} / \mathrm{s}\)
4 \(4.12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141199 The velocity of a particle moving along the \(\mathbf{x}\) axis varies as a function of time \(t\) as \(v(t)=\left(1-3 t^{2}+2 t^{3}\right)\) ms. If its position at \(t=0\) is \(x=0\) then at \(t=2 s\), its position is

1 \(1 \mathrm{~m}\)
2 \(2 \mathrm{~m}\)
3 \(4 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in One Dimensions

141200 At time \(t=0\), a particle leaves the origin and moves in the positive direction of the \(\mathrm{X}\)-axis. If the velocity of the particles varies as \(\overline{\mathbf{V}}(t)=\overline{\mathbf{V}}_{0}\left(1-\frac{\mathbf{t}}{\mathbf{t}_{0}}\right),\left|\overrightarrow{\mathbf{V}}_{\mathbf{0}}\right|=\mathbf{1 0 m} / \mathrm{s}\) and \(t_{0}=\mathbf{1 0} \mathrm{s}\), then the distance covered by the particle during the first \(20 \mathrm{~s}\) is:

1 \(200 \mathrm{~m}\)
2 \(100 \mathrm{~m}\)
3 \(0 \mathrm{~m}\)
4 \(400 \mathrm{~m}\)
Motion in One Dimensions

141201 For the following velocity-time graph, the average speed for the motion during first 80 seconds
original image

1 0
2 \(5 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(0.25 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141197 A cyclist traversed half the distance of a linear track with a velocity \(10 \mathrm{~m} / \mathrm{s}\). The remaining part of the track was covered with a velocity \(\vec{v}_{1}\) for half the time and a velocity \(\vec{v}_{2}\) for the other half of the time. If \(\vec{v}_{1}+\vec{v}_{2}=20 \mathrm{~m} / \mathrm{s}\), then the average velocity of the cyclist during the completion of the journey through the track is:

1 \(30 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(15 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141198 A car travels in a straight line along a road. Its distance ' \(x\) ' from a stop sign is given as a function of ' \(t\) ' by the equation \(x(t)=\alpha t+\beta t^{3}\), where \(\alpha=2.0 \mathrm{~m} / \mathrm{s}, \beta=0.01 \mathrm{~m} / \mathrm{s}^{3}\). Calculate the average velocity of the car in the time interval \(t\) \(=2.00 \mathrm{sec}\) to \(4.00 \mathrm{sec}\).

1 \(2.28 \mathrm{~m} / \mathrm{s}\)
2 \(4.94 \mathrm{~m} / \mathrm{s}\)
3 \(3.34 \mathrm{~m} / \mathrm{s}\)
4 \(4.12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141199 The velocity of a particle moving along the \(\mathbf{x}\) axis varies as a function of time \(t\) as \(v(t)=\left(1-3 t^{2}+2 t^{3}\right)\) ms. If its position at \(t=0\) is \(x=0\) then at \(t=2 s\), its position is

1 \(1 \mathrm{~m}\)
2 \(2 \mathrm{~m}\)
3 \(4 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in One Dimensions

141200 At time \(t=0\), a particle leaves the origin and moves in the positive direction of the \(\mathrm{X}\)-axis. If the velocity of the particles varies as \(\overline{\mathbf{V}}(t)=\overline{\mathbf{V}}_{0}\left(1-\frac{\mathbf{t}}{\mathbf{t}_{0}}\right),\left|\overrightarrow{\mathbf{V}}_{\mathbf{0}}\right|=\mathbf{1 0 m} / \mathrm{s}\) and \(t_{0}=\mathbf{1 0} \mathrm{s}\), then the distance covered by the particle during the first \(20 \mathrm{~s}\) is:

1 \(200 \mathrm{~m}\)
2 \(100 \mathrm{~m}\)
3 \(0 \mathrm{~m}\)
4 \(400 \mathrm{~m}\)
Motion in One Dimensions

141201 For the following velocity-time graph, the average speed for the motion during first 80 seconds
original image

1 0
2 \(5 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(0.25 \mathrm{~m} / \mathrm{s}\)
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Motion in One Dimensions

141197 A cyclist traversed half the distance of a linear track with a velocity \(10 \mathrm{~m} / \mathrm{s}\). The remaining part of the track was covered with a velocity \(\vec{v}_{1}\) for half the time and a velocity \(\vec{v}_{2}\) for the other half of the time. If \(\vec{v}_{1}+\vec{v}_{2}=20 \mathrm{~m} / \mathrm{s}\), then the average velocity of the cyclist during the completion of the journey through the track is:

1 \(30 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(15 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141198 A car travels in a straight line along a road. Its distance ' \(x\) ' from a stop sign is given as a function of ' \(t\) ' by the equation \(x(t)=\alpha t+\beta t^{3}\), where \(\alpha=2.0 \mathrm{~m} / \mathrm{s}, \beta=0.01 \mathrm{~m} / \mathrm{s}^{3}\). Calculate the average velocity of the car in the time interval \(t\) \(=2.00 \mathrm{sec}\) to \(4.00 \mathrm{sec}\).

1 \(2.28 \mathrm{~m} / \mathrm{s}\)
2 \(4.94 \mathrm{~m} / \mathrm{s}\)
3 \(3.34 \mathrm{~m} / \mathrm{s}\)
4 \(4.12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141199 The velocity of a particle moving along the \(\mathbf{x}\) axis varies as a function of time \(t\) as \(v(t)=\left(1-3 t^{2}+2 t^{3}\right)\) ms. If its position at \(t=0\) is \(x=0\) then at \(t=2 s\), its position is

1 \(1 \mathrm{~m}\)
2 \(2 \mathrm{~m}\)
3 \(4 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in One Dimensions

141200 At time \(t=0\), a particle leaves the origin and moves in the positive direction of the \(\mathrm{X}\)-axis. If the velocity of the particles varies as \(\overline{\mathbf{V}}(t)=\overline{\mathbf{V}}_{0}\left(1-\frac{\mathbf{t}}{\mathbf{t}_{0}}\right),\left|\overrightarrow{\mathbf{V}}_{\mathbf{0}}\right|=\mathbf{1 0 m} / \mathrm{s}\) and \(t_{0}=\mathbf{1 0} \mathrm{s}\), then the distance covered by the particle during the first \(20 \mathrm{~s}\) is:

1 \(200 \mathrm{~m}\)
2 \(100 \mathrm{~m}\)
3 \(0 \mathrm{~m}\)
4 \(400 \mathrm{~m}\)
Motion in One Dimensions

141201 For the following velocity-time graph, the average speed for the motion during first 80 seconds
original image

1 0
2 \(5 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(0.25 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141197 A cyclist traversed half the distance of a linear track with a velocity \(10 \mathrm{~m} / \mathrm{s}\). The remaining part of the track was covered with a velocity \(\vec{v}_{1}\) for half the time and a velocity \(\vec{v}_{2}\) for the other half of the time. If \(\vec{v}_{1}+\vec{v}_{2}=20 \mathrm{~m} / \mathrm{s}\), then the average velocity of the cyclist during the completion of the journey through the track is:

1 \(30 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(15 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141198 A car travels in a straight line along a road. Its distance ' \(x\) ' from a stop sign is given as a function of ' \(t\) ' by the equation \(x(t)=\alpha t+\beta t^{3}\), where \(\alpha=2.0 \mathrm{~m} / \mathrm{s}, \beta=0.01 \mathrm{~m} / \mathrm{s}^{3}\). Calculate the average velocity of the car in the time interval \(t\) \(=2.00 \mathrm{sec}\) to \(4.00 \mathrm{sec}\).

1 \(2.28 \mathrm{~m} / \mathrm{s}\)
2 \(4.94 \mathrm{~m} / \mathrm{s}\)
3 \(3.34 \mathrm{~m} / \mathrm{s}\)
4 \(4.12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141199 The velocity of a particle moving along the \(\mathbf{x}\) axis varies as a function of time \(t\) as \(v(t)=\left(1-3 t^{2}+2 t^{3}\right)\) ms. If its position at \(t=0\) is \(x=0\) then at \(t=2 s\), its position is

1 \(1 \mathrm{~m}\)
2 \(2 \mathrm{~m}\)
3 \(4 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in One Dimensions

141200 At time \(t=0\), a particle leaves the origin and moves in the positive direction of the \(\mathrm{X}\)-axis. If the velocity of the particles varies as \(\overline{\mathbf{V}}(t)=\overline{\mathbf{V}}_{0}\left(1-\frac{\mathbf{t}}{\mathbf{t}_{0}}\right),\left|\overrightarrow{\mathbf{V}}_{\mathbf{0}}\right|=\mathbf{1 0 m} / \mathrm{s}\) and \(t_{0}=\mathbf{1 0} \mathrm{s}\), then the distance covered by the particle during the first \(20 \mathrm{~s}\) is:

1 \(200 \mathrm{~m}\)
2 \(100 \mathrm{~m}\)
3 \(0 \mathrm{~m}\)
4 \(400 \mathrm{~m}\)
Motion in One Dimensions

141201 For the following velocity-time graph, the average speed for the motion during first 80 seconds
original image

1 0
2 \(5 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(0.25 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141197 A cyclist traversed half the distance of a linear track with a velocity \(10 \mathrm{~m} / \mathrm{s}\). The remaining part of the track was covered with a velocity \(\vec{v}_{1}\) for half the time and a velocity \(\vec{v}_{2}\) for the other half of the time. If \(\vec{v}_{1}+\vec{v}_{2}=20 \mathrm{~m} / \mathrm{s}\), then the average velocity of the cyclist during the completion of the journey through the track is:

1 \(30 \mathrm{~m} / \mathrm{s}\)
2 \(20 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(15 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141198 A car travels in a straight line along a road. Its distance ' \(x\) ' from a stop sign is given as a function of ' \(t\) ' by the equation \(x(t)=\alpha t+\beta t^{3}\), where \(\alpha=2.0 \mathrm{~m} / \mathrm{s}, \beta=0.01 \mathrm{~m} / \mathrm{s}^{3}\). Calculate the average velocity of the car in the time interval \(t\) \(=2.00 \mathrm{sec}\) to \(4.00 \mathrm{sec}\).

1 \(2.28 \mathrm{~m} / \mathrm{s}\)
2 \(4.94 \mathrm{~m} / \mathrm{s}\)
3 \(3.34 \mathrm{~m} / \mathrm{s}\)
4 \(4.12 \mathrm{~m} / \mathrm{s}\)
Motion in One Dimensions

141199 The velocity of a particle moving along the \(\mathbf{x}\) axis varies as a function of time \(t\) as \(v(t)=\left(1-3 t^{2}+2 t^{3}\right)\) ms. If its position at \(t=0\) is \(x=0\) then at \(t=2 s\), its position is

1 \(1 \mathrm{~m}\)
2 \(2 \mathrm{~m}\)
3 \(4 \mathrm{~m}\)
4 \(18 \mathrm{~m}\)
Motion in One Dimensions

141200 At time \(t=0\), a particle leaves the origin and moves in the positive direction of the \(\mathrm{X}\)-axis. If the velocity of the particles varies as \(\overline{\mathbf{V}}(t)=\overline{\mathbf{V}}_{0}\left(1-\frac{\mathbf{t}}{\mathbf{t}_{0}}\right),\left|\overrightarrow{\mathbf{V}}_{\mathbf{0}}\right|=\mathbf{1 0 m} / \mathrm{s}\) and \(t_{0}=\mathbf{1 0} \mathrm{s}\), then the distance covered by the particle during the first \(20 \mathrm{~s}\) is:

1 \(200 \mathrm{~m}\)
2 \(100 \mathrm{~m}\)
3 \(0 \mathrm{~m}\)
4 \(400 \mathrm{~m}\)
Motion in One Dimensions

141201 For the following velocity-time graph, the average speed for the motion during first 80 seconds
original image

1 0
2 \(5 \mathrm{~m} / \mathrm{s}\)
3 \(10 \mathrm{~m} / \mathrm{s}\)
4 \(0.25 \mathrm{~m} / \mathrm{s}\)