00. Distance and Displacement
Motion in One Dimensions

141282 A metro trains starts from rest and in five seconds achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141283 The v-t graph for a particle is as shown. The distance travelled in the first four seconds is :
original image

1 \(12 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(20 \mathrm{~m}\)
4 \(24 \mathrm{~m}\)
Motion in One Dimensions

141284 A body dropped from the top of a tower covers a distance \(7 x\) in the last second of its journey, where \(x\) is the distance covered in first second. How much time does it take to reach the ground?

1 \(3 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(5 \mathrm{~s}\)
4 \(6 \mathrm{~s}\)
Motion in One Dimensions

141285 At what angle must the two forces \((x+y)\) and \((x-y)\) act so that the resultant may be \(\sqrt{\left(x^{2}+y^{2}\right)}\) ?

1 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{2\left(x^{2}-y^{2}\right)}\right]\)
2 \(\cos ^{-1}\left[\frac{-2\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}}\right]\)
3 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{\left(x^{2}-y^{2}\right)}\right]\)
4 \(\cos ^{-1}\left[-\frac{\left(x^{2}-y^{2}\right)}{\left(x^{2}+y^{2}\right)}\right]\)
Motion in One Dimensions

141282 A metro trains starts from rest and in five seconds achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141283 The v-t graph for a particle is as shown. The distance travelled in the first four seconds is :
original image

1 \(12 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(20 \mathrm{~m}\)
4 \(24 \mathrm{~m}\)
Motion in One Dimensions

141284 A body dropped from the top of a tower covers a distance \(7 x\) in the last second of its journey, where \(x\) is the distance covered in first second. How much time does it take to reach the ground?

1 \(3 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(5 \mathrm{~s}\)
4 \(6 \mathrm{~s}\)
Motion in One Dimensions

141285 At what angle must the two forces \((x+y)\) and \((x-y)\) act so that the resultant may be \(\sqrt{\left(x^{2}+y^{2}\right)}\) ?

1 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{2\left(x^{2}-y^{2}\right)}\right]\)
2 \(\cos ^{-1}\left[\frac{-2\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}}\right]\)
3 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{\left(x^{2}-y^{2}\right)}\right]\)
4 \(\cos ^{-1}\left[-\frac{\left(x^{2}-y^{2}\right)}{\left(x^{2}+y^{2}\right)}\right]\)
Motion in One Dimensions

141282 A metro trains starts from rest and in five seconds achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141283 The v-t graph for a particle is as shown. The distance travelled in the first four seconds is :
original image

1 \(12 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(20 \mathrm{~m}\)
4 \(24 \mathrm{~m}\)
Motion in One Dimensions

141284 A body dropped from the top of a tower covers a distance \(7 x\) in the last second of its journey, where \(x\) is the distance covered in first second. How much time does it take to reach the ground?

1 \(3 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(5 \mathrm{~s}\)
4 \(6 \mathrm{~s}\)
Motion in One Dimensions

141285 At what angle must the two forces \((x+y)\) and \((x-y)\) act so that the resultant may be \(\sqrt{\left(x^{2}+y^{2}\right)}\) ?

1 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{2\left(x^{2}-y^{2}\right)}\right]\)
2 \(\cos ^{-1}\left[\frac{-2\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}}\right]\)
3 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{\left(x^{2}-y^{2}\right)}\right]\)
4 \(\cos ^{-1}\left[-\frac{\left(x^{2}-y^{2}\right)}{\left(x^{2}+y^{2}\right)}\right]\)
Motion in One Dimensions

141282 A metro trains starts from rest and in five seconds achieves \(108 \mathrm{~km} / \mathrm{h}\). After that it moves with constant velocity and comes to rest after travelling \(45 \mathrm{~m}\) with uniform retardation. If total distance travelled is \(395 \mathrm{~m}\), find total time of travelling.

1 \(12.2 \mathrm{~s}\)
2 \(15.3 \mathrm{~s}\)
3 \(9 \mathrm{~s}\)
4 \(17.2 \mathrm{~s}\)
Motion in One Dimensions

141283 The v-t graph for a particle is as shown. The distance travelled in the first four seconds is :
original image

1 \(12 \mathrm{~m}\)
2 \(16 \mathrm{~m}\)
3 \(20 \mathrm{~m}\)
4 \(24 \mathrm{~m}\)
Motion in One Dimensions

141284 A body dropped from the top of a tower covers a distance \(7 x\) in the last second of its journey, where \(x\) is the distance covered in first second. How much time does it take to reach the ground?

1 \(3 \mathrm{~s}\)
2 \(4 \mathrm{~s}\)
3 \(5 \mathrm{~s}\)
4 \(6 \mathrm{~s}\)
Motion in One Dimensions

141285 At what angle must the two forces \((x+y)\) and \((x-y)\) act so that the resultant may be \(\sqrt{\left(x^{2}+y^{2}\right)}\) ?

1 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{2\left(x^{2}-y^{2}\right)}\right]\)
2 \(\cos ^{-1}\left[\frac{-2\left(x^{2}-y^{2}\right)}{x^{2}+y^{2}}\right]\)
3 \(\cos ^{-1}\left[-\frac{\left(x^{2}+y^{2}\right)}{\left(x^{2}-y^{2}\right)}\right]\)
4 \(\cos ^{-1}\left[-\frac{\left(x^{2}-y^{2}\right)}{\left(x^{2}+y^{2}\right)}\right]\)