03. Equation of Motion
Motion in One Dimensions

141758 A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \(1 \mathrm{~ms}^{-2}\), the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is

1 \(8 \mathrm{~ms}^{-1}\)
2 \(5 \mathrm{~ms}^{-1}\)
3 \(12 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141759 If a car at rest accelerated uniformly to a speed of \(144 \mathrm{~km} /\) hour in 20 second it covers a distance:

1 \(400 \mathrm{~m}\)
2 \(1440 \mathrm{~m}\)
3 \(2880 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141761 The acceleration \(a\) of a particle starting from rest varies with time according to relation a \(=\alpha t+\beta\). The velocity of the particle after a time \(t\) will be

1 \(\frac{\alpha t^{2}}{2}+\beta\)
2 \(\frac{\alpha t^{2}}{2}+\beta t\)
3 \(\alpha t^{2}+\frac{1}{2} \beta t\)
4 \(\frac{\left(\alpha \mathrm{t}^{2}+\beta\right)}{2}\)
Motion in One Dimensions

141762 A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the \(4^{\text {th }}\) second compared to that in the \(3^{\text {rd }}\) second is

1 \(33 \%\)
2 \(40 \%\)
3 \(66 \%\)
4 \(77 \%\)
Motion in One Dimensions

141763 A particle is travelling along a straight line \(O X\). The distance \(x\) (in meter) of the particle from \(O\) at a time \(t\) is given by \(x=37+27 t-t^{3}\), where \(t\) is time in seconds. The distance of the particle from \(O\) when it comes to rest is

1 \(81 \mathrm{~m}\)
2 \(91 \mathrm{~m}\)
3 \(101 \mathrm{~m}\)
4 \(111 \mathrm{~m}\)
Motion in One Dimensions

141758 A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \(1 \mathrm{~ms}^{-2}\), the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is

1 \(8 \mathrm{~ms}^{-1}\)
2 \(5 \mathrm{~ms}^{-1}\)
3 \(12 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141759 If a car at rest accelerated uniformly to a speed of \(144 \mathrm{~km} /\) hour in 20 second it covers a distance:

1 \(400 \mathrm{~m}\)
2 \(1440 \mathrm{~m}\)
3 \(2880 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141761 The acceleration \(a\) of a particle starting from rest varies with time according to relation a \(=\alpha t+\beta\). The velocity of the particle after a time \(t\) will be

1 \(\frac{\alpha t^{2}}{2}+\beta\)
2 \(\frac{\alpha t^{2}}{2}+\beta t\)
3 \(\alpha t^{2}+\frac{1}{2} \beta t\)
4 \(\frac{\left(\alpha \mathrm{t}^{2}+\beta\right)}{2}\)
Motion in One Dimensions

141762 A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the \(4^{\text {th }}\) second compared to that in the \(3^{\text {rd }}\) second is

1 \(33 \%\)
2 \(40 \%\)
3 \(66 \%\)
4 \(77 \%\)
Motion in One Dimensions

141763 A particle is travelling along a straight line \(O X\). The distance \(x\) (in meter) of the particle from \(O\) at a time \(t\) is given by \(x=37+27 t-t^{3}\), where \(t\) is time in seconds. The distance of the particle from \(O\) when it comes to rest is

1 \(81 \mathrm{~m}\)
2 \(91 \mathrm{~m}\)
3 \(101 \mathrm{~m}\)
4 \(111 \mathrm{~m}\)
Motion in One Dimensions

141758 A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \(1 \mathrm{~ms}^{-2}\), the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is

1 \(8 \mathrm{~ms}^{-1}\)
2 \(5 \mathrm{~ms}^{-1}\)
3 \(12 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141759 If a car at rest accelerated uniformly to a speed of \(144 \mathrm{~km} /\) hour in 20 second it covers a distance:

1 \(400 \mathrm{~m}\)
2 \(1440 \mathrm{~m}\)
3 \(2880 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141761 The acceleration \(a\) of a particle starting from rest varies with time according to relation a \(=\alpha t+\beta\). The velocity of the particle after a time \(t\) will be

1 \(\frac{\alpha t^{2}}{2}+\beta\)
2 \(\frac{\alpha t^{2}}{2}+\beta t\)
3 \(\alpha t^{2}+\frac{1}{2} \beta t\)
4 \(\frac{\left(\alpha \mathrm{t}^{2}+\beta\right)}{2}\)
Motion in One Dimensions

141762 A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the \(4^{\text {th }}\) second compared to that in the \(3^{\text {rd }}\) second is

1 \(33 \%\)
2 \(40 \%\)
3 \(66 \%\)
4 \(77 \%\)
Motion in One Dimensions

141763 A particle is travelling along a straight line \(O X\). The distance \(x\) (in meter) of the particle from \(O\) at a time \(t\) is given by \(x=37+27 t-t^{3}\), where \(t\) is time in seconds. The distance of the particle from \(O\) when it comes to rest is

1 \(81 \mathrm{~m}\)
2 \(91 \mathrm{~m}\)
3 \(101 \mathrm{~m}\)
4 \(111 \mathrm{~m}\)
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Motion in One Dimensions

141758 A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \(1 \mathrm{~ms}^{-2}\), the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is

1 \(8 \mathrm{~ms}^{-1}\)
2 \(5 \mathrm{~ms}^{-1}\)
3 \(12 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141759 If a car at rest accelerated uniformly to a speed of \(144 \mathrm{~km} /\) hour in 20 second it covers a distance:

1 \(400 \mathrm{~m}\)
2 \(1440 \mathrm{~m}\)
3 \(2880 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141761 The acceleration \(a\) of a particle starting from rest varies with time according to relation a \(=\alpha t+\beta\). The velocity of the particle after a time \(t\) will be

1 \(\frac{\alpha t^{2}}{2}+\beta\)
2 \(\frac{\alpha t^{2}}{2}+\beta t\)
3 \(\alpha t^{2}+\frac{1}{2} \beta t\)
4 \(\frac{\left(\alpha \mathrm{t}^{2}+\beta\right)}{2}\)
Motion in One Dimensions

141762 A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the \(4^{\text {th }}\) second compared to that in the \(3^{\text {rd }}\) second is

1 \(33 \%\)
2 \(40 \%\)
3 \(66 \%\)
4 \(77 \%\)
Motion in One Dimensions

141763 A particle is travelling along a straight line \(O X\). The distance \(x\) (in meter) of the particle from \(O\) at a time \(t\) is given by \(x=37+27 t-t^{3}\), where \(t\) is time in seconds. The distance of the particle from \(O\) when it comes to rest is

1 \(81 \mathrm{~m}\)
2 \(91 \mathrm{~m}\)
3 \(101 \mathrm{~m}\)
4 \(111 \mathrm{~m}\)
Motion in One Dimensions

141758 A student is standing at a distance of 50 metre from the bus. As soon as the bus begins its motion with an acceleration of \(1 \mathrm{~ms}^{-2}\), the student starts running towards the bus with a uniform velocity \(u\). Assuming the motion to be along a straight road, the minimum value of \(u\), so that the student is able to catch the bus is

1 \(8 \mathrm{~ms}^{-1}\)
2 \(5 \mathrm{~ms}^{-1}\)
3 \(12 \mathrm{~ms}^{-1}\)
4 \(10 \mathrm{~ms}^{-1}\)
Motion in One Dimensions

141759 If a car at rest accelerated uniformly to a speed of \(144 \mathrm{~km} /\) hour in 20 second it covers a distance:

1 \(400 \mathrm{~m}\)
2 \(1440 \mathrm{~m}\)
3 \(2880 \mathrm{~m}\)
4 \(25 \mathrm{~m}\)
Motion in One Dimensions

141761 The acceleration \(a\) of a particle starting from rest varies with time according to relation a \(=\alpha t+\beta\). The velocity of the particle after a time \(t\) will be

1 \(\frac{\alpha t^{2}}{2}+\beta\)
2 \(\frac{\alpha t^{2}}{2}+\beta t\)
3 \(\alpha t^{2}+\frac{1}{2} \beta t\)
4 \(\frac{\left(\alpha \mathrm{t}^{2}+\beta\right)}{2}\)
Motion in One Dimensions

141762 A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the \(4^{\text {th }}\) second compared to that in the \(3^{\text {rd }}\) second is

1 \(33 \%\)
2 \(40 \%\)
3 \(66 \%\)
4 \(77 \%\)
Motion in One Dimensions

141763 A particle is travelling along a straight line \(O X\). The distance \(x\) (in meter) of the particle from \(O\) at a time \(t\) is given by \(x=37+27 t-t^{3}\), where \(t\) is time in seconds. The distance of the particle from \(O\) when it comes to rest is

1 \(81 \mathrm{~m}\)
2 \(91 \mathrm{~m}\)
3 \(101 \mathrm{~m}\)
4 \(111 \mathrm{~m}\)