00. Distance and Displacement
Motion in One Dimensions

141352 A particle of unit mass undergoes onedimensional motion such that its velocity varies according to \(\mathbf{v}(\mathbf{x})=\beta \mathbf{x}^{-2 \mathrm{n}}\) where, \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\), is given by

1 \(-2 n \beta^{2} x^{-2 n-1}\)
2 \(-2 \mathrm{n} \beta^{2} x^{-4 n-1}\)
3 \(-2 \beta^{2} x^{-2 n+1}\)
4 \(-2 n \beta^{2} e^{-4 n+1}\)
Motion in One Dimensions

141353 The motion of a particle along a straight line is described by equation \(x=8+12 t-t^{3}\) where, \(x\) is in metre and \(t\) in sec. The retardation of the particle when its velocity becomes zero, is

1 \(24 \mathrm{~ms}^{-2}\)
2 zero
3 \(6 \mathrm{~ms}^{-2}\)
4 \(12 \mathrm{~ms}^{-2}\)
Motion in One Dimensions

141354 A body is moving with velocity \(30 \mathrm{~m} / \mathrm{s}\) towards East. After 10s, its velocity becomes \(40 \mathrm{~m} / \mathrm{s}\) towards North. The average acceleration of the body is

1 \(7 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(\sqrt{7} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(1 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141355 A particle moves a distance \(x\) in time \(t\) according to the equation \(x=(t+5)^{-1}\). The acceleration of particle is proportional to

1 (velocity) \()^{3 / 2}\)
2 (distance) \(^{2}\)
3 (distance) \(^{-2}\)
4 (velocity) \(^{2 / 3}\)
Motion in One Dimensions

141356 A bus is moving with a speed of \(10 \mathrm{~ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100 \mathrm{~s}\). If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1 \(20 \mathrm{~ms}^{-1}\)
2 \(40 \mathrm{~ms}^{-1}\)
3 \(25 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141352 A particle of unit mass undergoes onedimensional motion such that its velocity varies according to \(\mathbf{v}(\mathbf{x})=\beta \mathbf{x}^{-2 \mathrm{n}}\) where, \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\), is given by

1 \(-2 n \beta^{2} x^{-2 n-1}\)
2 \(-2 \mathrm{n} \beta^{2} x^{-4 n-1}\)
3 \(-2 \beta^{2} x^{-2 n+1}\)
4 \(-2 n \beta^{2} e^{-4 n+1}\)
Motion in One Dimensions

141353 The motion of a particle along a straight line is described by equation \(x=8+12 t-t^{3}\) where, \(x\) is in metre and \(t\) in sec. The retardation of the particle when its velocity becomes zero, is

1 \(24 \mathrm{~ms}^{-2}\)
2 zero
3 \(6 \mathrm{~ms}^{-2}\)
4 \(12 \mathrm{~ms}^{-2}\)
Motion in One Dimensions

141354 A body is moving with velocity \(30 \mathrm{~m} / \mathrm{s}\) towards East. After 10s, its velocity becomes \(40 \mathrm{~m} / \mathrm{s}\) towards North. The average acceleration of the body is

1 \(7 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(\sqrt{7} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(1 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141355 A particle moves a distance \(x\) in time \(t\) according to the equation \(x=(t+5)^{-1}\). The acceleration of particle is proportional to

1 (velocity) \()^{3 / 2}\)
2 (distance) \(^{2}\)
3 (distance) \(^{-2}\)
4 (velocity) \(^{2 / 3}\)
Motion in One Dimensions

141356 A bus is moving with a speed of \(10 \mathrm{~ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100 \mathrm{~s}\). If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1 \(20 \mathrm{~ms}^{-1}\)
2 \(40 \mathrm{~ms}^{-1}\)
3 \(25 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141352 A particle of unit mass undergoes onedimensional motion such that its velocity varies according to \(\mathbf{v}(\mathbf{x})=\beta \mathbf{x}^{-2 \mathrm{n}}\) where, \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\), is given by

1 \(-2 n \beta^{2} x^{-2 n-1}\)
2 \(-2 \mathrm{n} \beta^{2} x^{-4 n-1}\)
3 \(-2 \beta^{2} x^{-2 n+1}\)
4 \(-2 n \beta^{2} e^{-4 n+1}\)
Motion in One Dimensions

141353 The motion of a particle along a straight line is described by equation \(x=8+12 t-t^{3}\) where, \(x\) is in metre and \(t\) in sec. The retardation of the particle when its velocity becomes zero, is

1 \(24 \mathrm{~ms}^{-2}\)
2 zero
3 \(6 \mathrm{~ms}^{-2}\)
4 \(12 \mathrm{~ms}^{-2}\)
Motion in One Dimensions

141354 A body is moving with velocity \(30 \mathrm{~m} / \mathrm{s}\) towards East. After 10s, its velocity becomes \(40 \mathrm{~m} / \mathrm{s}\) towards North. The average acceleration of the body is

1 \(7 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(\sqrt{7} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(1 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141355 A particle moves a distance \(x\) in time \(t\) according to the equation \(x=(t+5)^{-1}\). The acceleration of particle is proportional to

1 (velocity) \()^{3 / 2}\)
2 (distance) \(^{2}\)
3 (distance) \(^{-2}\)
4 (velocity) \(^{2 / 3}\)
Motion in One Dimensions

141356 A bus is moving with a speed of \(10 \mathrm{~ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100 \mathrm{~s}\). If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1 \(20 \mathrm{~ms}^{-1}\)
2 \(40 \mathrm{~ms}^{-1}\)
3 \(25 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
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Motion in One Dimensions

141352 A particle of unit mass undergoes onedimensional motion such that its velocity varies according to \(\mathbf{v}(\mathbf{x})=\beta \mathbf{x}^{-2 \mathrm{n}}\) where, \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\), is given by

1 \(-2 n \beta^{2} x^{-2 n-1}\)
2 \(-2 \mathrm{n} \beta^{2} x^{-4 n-1}\)
3 \(-2 \beta^{2} x^{-2 n+1}\)
4 \(-2 n \beta^{2} e^{-4 n+1}\)
Motion in One Dimensions

141353 The motion of a particle along a straight line is described by equation \(x=8+12 t-t^{3}\) where, \(x\) is in metre and \(t\) in sec. The retardation of the particle when its velocity becomes zero, is

1 \(24 \mathrm{~ms}^{-2}\)
2 zero
3 \(6 \mathrm{~ms}^{-2}\)
4 \(12 \mathrm{~ms}^{-2}\)
Motion in One Dimensions

141354 A body is moving with velocity \(30 \mathrm{~m} / \mathrm{s}\) towards East. After 10s, its velocity becomes \(40 \mathrm{~m} / \mathrm{s}\) towards North. The average acceleration of the body is

1 \(7 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(\sqrt{7} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(1 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141355 A particle moves a distance \(x\) in time \(t\) according to the equation \(x=(t+5)^{-1}\). The acceleration of particle is proportional to

1 (velocity) \()^{3 / 2}\)
2 (distance) \(^{2}\)
3 (distance) \(^{-2}\)
4 (velocity) \(^{2 / 3}\)
Motion in One Dimensions

141356 A bus is moving with a speed of \(10 \mathrm{~ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100 \mathrm{~s}\). If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1 \(20 \mathrm{~ms}^{-1}\)
2 \(40 \mathrm{~ms}^{-1}\)
3 \(25 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141352 A particle of unit mass undergoes onedimensional motion such that its velocity varies according to \(\mathbf{v}(\mathbf{x})=\beta \mathbf{x}^{-2 \mathrm{n}}\) where, \(\beta\) and \(n\) are constants and \(x\) is the position of the particle. The acceleration of the particle as a function of \(x\), is given by

1 \(-2 n \beta^{2} x^{-2 n-1}\)
2 \(-2 \mathrm{n} \beta^{2} x^{-4 n-1}\)
3 \(-2 \beta^{2} x^{-2 n+1}\)
4 \(-2 n \beta^{2} e^{-4 n+1}\)
Motion in One Dimensions

141353 The motion of a particle along a straight line is described by equation \(x=8+12 t-t^{3}\) where, \(x\) is in metre and \(t\) in sec. The retardation of the particle when its velocity becomes zero, is

1 \(24 \mathrm{~ms}^{-2}\)
2 zero
3 \(6 \mathrm{~ms}^{-2}\)
4 \(12 \mathrm{~ms}^{-2}\)
Motion in One Dimensions

141354 A body is moving with velocity \(30 \mathrm{~m} / \mathrm{s}\) towards East. After 10s, its velocity becomes \(40 \mathrm{~m} / \mathrm{s}\) towards North. The average acceleration of the body is

1 \(7 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(\sqrt{7} \mathrm{~m} / \mathrm{s}^{2}\)
3 \(5 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(1 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141355 A particle moves a distance \(x\) in time \(t\) according to the equation \(x=(t+5)^{-1}\). The acceleration of particle is proportional to

1 (velocity) \()^{3 / 2}\)
2 (distance) \(^{2}\)
3 (distance) \(^{-2}\)
4 (velocity) \(^{2 / 3}\)
Motion in One Dimensions

141356 A bus is moving with a speed of \(10 \mathrm{~ms}^{-1}\) on a straight road. A scooterist wishes to overtake the bus in \(100 \mathrm{~s}\). If the bus is at a distance of 1 km from the scooterist, with what speed should the scooterist chase the bus?

1 \(20 \mathrm{~ms}^{-1}\)
2 \(40 \mathrm{~ms}^{-1}\)
3 \(25 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)