00. Distance and Displacement
Motion in One Dimensions

141376 An object moving with a speed of \(6.25 \mathrm{~m} / \mathrm{s}\), is decelerated at a rate given by \(\mathrm{dv} / \mathrm{dt}=-2.5 \sqrt{\mathrm{v}}\) where \(v\) is the instantaneous speed(d) The time taken by the object to come to rest, would be

1 \(2 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141377 The equation of motion of a body is \(\frac{d v(t)}{d t}=9-3 v(t)\), where \(v(t)\), where \(v(t)\) is the speed (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t\) (in second). If the body was at rest at \(t=0\), then which of the following is correct?

1 The terminal speed is \(3 \mathrm{~m} / \mathrm{s}\)
2 Initial acceleration is \(9 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(v(\mathrm{t})=3\left(1-\mathrm{e}^{-3 \mathrm{t}}\right)\)
4 All of these are correct
Motion in One Dimensions

141378 A particle moves in the \(x\)-y plane with velocity \(v_{x}=8 t-2\) and \(v_{y}=2\). If it passes through the point \(x=14\) and \(y=4\) at \(t=2 \mathrm{~s}\), then the equation of the path will be

1 \(x=y^{2}-y+2\)
2 \(x=2 y^{2}+2 y-3\)
3 \(x=3 y^{2}+5\)
4 None of the above
Motion in One Dimensions

141379 Engine of a vehicle can give it an acceleration of \(1 \mathrm{~m} / \mathrm{s}^{2}\), while the brake of the vehicle can retard it at \(8 \mathrm{~m} / \mathrm{s}^{2}\). Then the minimum time in which the vehicle can complete a journey of \(600 \mathrm{~m}\) will be.

1 \(80 \mathrm{~s}\)
2 \(60 \mathrm{~s}\)
3 \(40 \mathrm{~s}\)
4 None of the above
Motion in One Dimensions

141376 An object moving with a speed of \(6.25 \mathrm{~m} / \mathrm{s}\), is decelerated at a rate given by \(\mathrm{dv} / \mathrm{dt}=-2.5 \sqrt{\mathrm{v}}\) where \(v\) is the instantaneous speed(d) The time taken by the object to come to rest, would be

1 \(2 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141377 The equation of motion of a body is \(\frac{d v(t)}{d t}=9-3 v(t)\), where \(v(t)\), where \(v(t)\) is the speed (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t\) (in second). If the body was at rest at \(t=0\), then which of the following is correct?

1 The terminal speed is \(3 \mathrm{~m} / \mathrm{s}\)
2 Initial acceleration is \(9 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(v(\mathrm{t})=3\left(1-\mathrm{e}^{-3 \mathrm{t}}\right)\)
4 All of these are correct
Motion in One Dimensions

141378 A particle moves in the \(x\)-y plane with velocity \(v_{x}=8 t-2\) and \(v_{y}=2\). If it passes through the point \(x=14\) and \(y=4\) at \(t=2 \mathrm{~s}\), then the equation of the path will be

1 \(x=y^{2}-y+2\)
2 \(x=2 y^{2}+2 y-3\)
3 \(x=3 y^{2}+5\)
4 None of the above
Motion in One Dimensions

141379 Engine of a vehicle can give it an acceleration of \(1 \mathrm{~m} / \mathrm{s}^{2}\), while the brake of the vehicle can retard it at \(8 \mathrm{~m} / \mathrm{s}^{2}\). Then the minimum time in which the vehicle can complete a journey of \(600 \mathrm{~m}\) will be.

1 \(80 \mathrm{~s}\)
2 \(60 \mathrm{~s}\)
3 \(40 \mathrm{~s}\)
4 None of the above
Motion in One Dimensions

141376 An object moving with a speed of \(6.25 \mathrm{~m} / \mathrm{s}\), is decelerated at a rate given by \(\mathrm{dv} / \mathrm{dt}=-2.5 \sqrt{\mathrm{v}}\) where \(v\) is the instantaneous speed(d) The time taken by the object to come to rest, would be

1 \(2 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141377 The equation of motion of a body is \(\frac{d v(t)}{d t}=9-3 v(t)\), where \(v(t)\), where \(v(t)\) is the speed (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t\) (in second). If the body was at rest at \(t=0\), then which of the following is correct?

1 The terminal speed is \(3 \mathrm{~m} / \mathrm{s}\)
2 Initial acceleration is \(9 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(v(\mathrm{t})=3\left(1-\mathrm{e}^{-3 \mathrm{t}}\right)\)
4 All of these are correct
Motion in One Dimensions

141378 A particle moves in the \(x\)-y plane with velocity \(v_{x}=8 t-2\) and \(v_{y}=2\). If it passes through the point \(x=14\) and \(y=4\) at \(t=2 \mathrm{~s}\), then the equation of the path will be

1 \(x=y^{2}-y+2\)
2 \(x=2 y^{2}+2 y-3\)
3 \(x=3 y^{2}+5\)
4 None of the above
Motion in One Dimensions

141379 Engine of a vehicle can give it an acceleration of \(1 \mathrm{~m} / \mathrm{s}^{2}\), while the brake of the vehicle can retard it at \(8 \mathrm{~m} / \mathrm{s}^{2}\). Then the minimum time in which the vehicle can complete a journey of \(600 \mathrm{~m}\) will be.

1 \(80 \mathrm{~s}\)
2 \(60 \mathrm{~s}\)
3 \(40 \mathrm{~s}\)
4 None of the above
Motion in One Dimensions

141376 An object moving with a speed of \(6.25 \mathrm{~m} / \mathrm{s}\), is decelerated at a rate given by \(\mathrm{dv} / \mathrm{dt}=-2.5 \sqrt{\mathrm{v}}\) where \(v\) is the instantaneous speed(d) The time taken by the object to come to rest, would be

1 \(2 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(8 \mathrm{~s}\)
4 \(1 \mathrm{~s}\)
Motion in One Dimensions

141377 The equation of motion of a body is \(\frac{d v(t)}{d t}=9-3 v(t)\), where \(v(t)\), where \(v(t)\) is the speed (in \(\mathrm{m} / \mathrm{s}\) ) at time \(t\) (in second). If the body was at rest at \(t=0\), then which of the following is correct?

1 The terminal speed is \(3 \mathrm{~m} / \mathrm{s}\)
2 Initial acceleration is \(9 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(v(\mathrm{t})=3\left(1-\mathrm{e}^{-3 \mathrm{t}}\right)\)
4 All of these are correct
Motion in One Dimensions

141378 A particle moves in the \(x\)-y plane with velocity \(v_{x}=8 t-2\) and \(v_{y}=2\). If it passes through the point \(x=14\) and \(y=4\) at \(t=2 \mathrm{~s}\), then the equation of the path will be

1 \(x=y^{2}-y+2\)
2 \(x=2 y^{2}+2 y-3\)
3 \(x=3 y^{2}+5\)
4 None of the above
Motion in One Dimensions

141379 Engine of a vehicle can give it an acceleration of \(1 \mathrm{~m} / \mathrm{s}^{2}\), while the brake of the vehicle can retard it at \(8 \mathrm{~m} / \mathrm{s}^{2}\). Then the minimum time in which the vehicle can complete a journey of \(600 \mathrm{~m}\) will be.

1 \(80 \mathrm{~s}\)
2 \(60 \mathrm{~s}\)
3 \(40 \mathrm{~s}\)
4 None of the above