03. Equation of Motion
Motion in One Dimensions

141701 A NCC parade is going at a uniform speed of 9 \(\mathrm{km} / \mathrm{h}\) under a mango tree on which a monkey is sitting at a height of \(19.6 \mathrm{~m}\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :
[Given \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(5 \mathrm{~m}\)
2 \(10 \mathrm{~m}\)
3 \(19.8 \mathrm{~m}\)
4 \(24.5 \mathrm{~m}\)
Motion in One Dimensions

141702 A ball is spin with angular acceleration \(\alpha=6 t^{2}-\) \(2 t\), where \(t\) is in second and \(\alpha\) is in \(\operatorname{rads}^{-2}\). At \(t=0\), the ball has angular velocity of \(10 \mathrm{rads}^{-1}\) and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

1 \(\frac{3}{4} \mathrm{t}^{4}-\mathrm{t}^{2}+10 \mathrm{t}\)
2 \(\frac{t^{4}}{2}-\frac{t^{3}}{3}+10 t+4\)
3 \(\frac{2 \mathrm{t}^{4}}{3}-\frac{\mathrm{t}^{3}}{6}+10 \mathrm{t}+12\)
4 \(2 \mathrm{t}^{4}-\frac{\mathrm{t}^{3}}{2}+5 \mathrm{t}+4\)
Motion in One Dimensions

141703 Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line and their positions are represented by \(X_{P}(t)=\alpha t+\beta t^{2}\) and \(X_{Q}(t)=f t-t^{2}\). At what time, both the buses have same velocity?

1 \(\frac{\alpha-f}{1+\beta}\)
2 \(\frac{\alpha+f}{2(\beta-1)}\)
3 \(\frac{\alpha+\mathrm{f}}{2(1+\beta)}\)
4 \(\frac{f-\alpha}{2(1+\beta)}\)
Motion in One Dimensions

141704 A body starts from rest with uniform acceleration and moves in a straight line. If its speed after ' \(n\) ' seconds is ' \(v\) ', then the distance covered in the last \(2 \mathrm{sec}\) is,

1 \(\frac{2 \mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
2 \(\frac{\mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
3 \(\frac{\mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
4 \(\frac{2 \mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
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Motion in One Dimensions

141701 A NCC parade is going at a uniform speed of 9 \(\mathrm{km} / \mathrm{h}\) under a mango tree on which a monkey is sitting at a height of \(19.6 \mathrm{~m}\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :
[Given \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(5 \mathrm{~m}\)
2 \(10 \mathrm{~m}\)
3 \(19.8 \mathrm{~m}\)
4 \(24.5 \mathrm{~m}\)
Motion in One Dimensions

141702 A ball is spin with angular acceleration \(\alpha=6 t^{2}-\) \(2 t\), where \(t\) is in second and \(\alpha\) is in \(\operatorname{rads}^{-2}\). At \(t=0\), the ball has angular velocity of \(10 \mathrm{rads}^{-1}\) and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

1 \(\frac{3}{4} \mathrm{t}^{4}-\mathrm{t}^{2}+10 \mathrm{t}\)
2 \(\frac{t^{4}}{2}-\frac{t^{3}}{3}+10 t+4\)
3 \(\frac{2 \mathrm{t}^{4}}{3}-\frac{\mathrm{t}^{3}}{6}+10 \mathrm{t}+12\)
4 \(2 \mathrm{t}^{4}-\frac{\mathrm{t}^{3}}{2}+5 \mathrm{t}+4\)
Motion in One Dimensions

141703 Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line and their positions are represented by \(X_{P}(t)=\alpha t+\beta t^{2}\) and \(X_{Q}(t)=f t-t^{2}\). At what time, both the buses have same velocity?

1 \(\frac{\alpha-f}{1+\beta}\)
2 \(\frac{\alpha+f}{2(\beta-1)}\)
3 \(\frac{\alpha+\mathrm{f}}{2(1+\beta)}\)
4 \(\frac{f-\alpha}{2(1+\beta)}\)
Motion in One Dimensions

141704 A body starts from rest with uniform acceleration and moves in a straight line. If its speed after ' \(n\) ' seconds is ' \(v\) ', then the distance covered in the last \(2 \mathrm{sec}\) is,

1 \(\frac{2 \mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
2 \(\frac{\mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
3 \(\frac{\mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
4 \(\frac{2 \mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
Motion in One Dimensions

141701 A NCC parade is going at a uniform speed of 9 \(\mathrm{km} / \mathrm{h}\) under a mango tree on which a monkey is sitting at a height of \(19.6 \mathrm{~m}\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :
[Given \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(5 \mathrm{~m}\)
2 \(10 \mathrm{~m}\)
3 \(19.8 \mathrm{~m}\)
4 \(24.5 \mathrm{~m}\)
Motion in One Dimensions

141702 A ball is spin with angular acceleration \(\alpha=6 t^{2}-\) \(2 t\), where \(t\) is in second and \(\alpha\) is in \(\operatorname{rads}^{-2}\). At \(t=0\), the ball has angular velocity of \(10 \mathrm{rads}^{-1}\) and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

1 \(\frac{3}{4} \mathrm{t}^{4}-\mathrm{t}^{2}+10 \mathrm{t}\)
2 \(\frac{t^{4}}{2}-\frac{t^{3}}{3}+10 t+4\)
3 \(\frac{2 \mathrm{t}^{4}}{3}-\frac{\mathrm{t}^{3}}{6}+10 \mathrm{t}+12\)
4 \(2 \mathrm{t}^{4}-\frac{\mathrm{t}^{3}}{2}+5 \mathrm{t}+4\)
Motion in One Dimensions

141703 Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line and their positions are represented by \(X_{P}(t)=\alpha t+\beta t^{2}\) and \(X_{Q}(t)=f t-t^{2}\). At what time, both the buses have same velocity?

1 \(\frac{\alpha-f}{1+\beta}\)
2 \(\frac{\alpha+f}{2(\beta-1)}\)
3 \(\frac{\alpha+\mathrm{f}}{2(1+\beta)}\)
4 \(\frac{f-\alpha}{2(1+\beta)}\)
Motion in One Dimensions

141704 A body starts from rest with uniform acceleration and moves in a straight line. If its speed after ' \(n\) ' seconds is ' \(v\) ', then the distance covered in the last \(2 \mathrm{sec}\) is,

1 \(\frac{2 \mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
2 \(\frac{\mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
3 \(\frac{\mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
4 \(\frac{2 \mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
Motion in One Dimensions

141701 A NCC parade is going at a uniform speed of 9 \(\mathrm{km} / \mathrm{h}\) under a mango tree on which a monkey is sitting at a height of \(19.6 \mathrm{~m}\). At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is :
[Given \(g=9.8 \mathrm{~m} / \mathrm{s}^{2}\) ]

1 \(5 \mathrm{~m}\)
2 \(10 \mathrm{~m}\)
3 \(19.8 \mathrm{~m}\)
4 \(24.5 \mathrm{~m}\)
Motion in One Dimensions

141702 A ball is spin with angular acceleration \(\alpha=6 t^{2}-\) \(2 t\), where \(t\) is in second and \(\alpha\) is in \(\operatorname{rads}^{-2}\). At \(t=0\), the ball has angular velocity of \(10 \mathrm{rads}^{-1}\) and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

1 \(\frac{3}{4} \mathrm{t}^{4}-\mathrm{t}^{2}+10 \mathrm{t}\)
2 \(\frac{t^{4}}{2}-\frac{t^{3}}{3}+10 t+4\)
3 \(\frac{2 \mathrm{t}^{4}}{3}-\frac{\mathrm{t}^{3}}{6}+10 \mathrm{t}+12\)
4 \(2 \mathrm{t}^{4}-\frac{\mathrm{t}^{3}}{2}+5 \mathrm{t}+4\)
Motion in One Dimensions

141703 Two buses \(P\) and \(Q\) start from a point at the same time and move in a straight line and their positions are represented by \(X_{P}(t)=\alpha t+\beta t^{2}\) and \(X_{Q}(t)=f t-t^{2}\). At what time, both the buses have same velocity?

1 \(\frac{\alpha-f}{1+\beta}\)
2 \(\frac{\alpha+f}{2(\beta-1)}\)
3 \(\frac{\alpha+\mathrm{f}}{2(1+\beta)}\)
4 \(\frac{f-\alpha}{2(1+\beta)}\)
Motion in One Dimensions

141704 A body starts from rest with uniform acceleration and moves in a straight line. If its speed after ' \(n\) ' seconds is ' \(v\) ', then the distance covered in the last \(2 \mathrm{sec}\) is,

1 \(\frac{2 \mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
2 \(\frac{\mathrm{v}(\mathrm{n}+1)}{\mathrm{n}}\)
3 \(\frac{\mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)
4 \(\frac{2 \mathrm{v}(\mathrm{n}-1)}{\mathrm{n}}\)