01. Speed, Velocity and Acceleration
Motion in One Dimensions

141479 The speed time graph of a particle moving along a fixed direction is shown. The distance travelled by the particle in \(10 \mathrm{~s}\) is
original image

1 \(20 \mathrm{~m}\)
2 \(30 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(60 \mathrm{~m}\)
Motion in One Dimensions

141477 Assertion : A body may be accelerated even when it is moving uniformly.
Reason: When direction of motion of the body is changing, the body must have acceleration.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Motion in One Dimensions

141480 Consider a particle moving along the positive direction of \(\mathrm{X}\)-axis. The velocity of the particle is given by \(v=\alpha \sqrt{x}\) ( \(\alpha\) is a positive constant). At time \(t=0\), if the particle is located at \(x=0\), the time dependence of the velocity and the acceleration of the particle are respectively

1 \(\frac{\alpha^{2}}{2}\) tand \(\frac{\alpha^{2}}{2}\)
2 \(\alpha^{2} t\) and \(\alpha^{2}\)
3 \(\frac{\alpha}{2} \mathrm{t}\) and \(\frac{\alpha}{2}\)
4 \(\frac{\alpha^{2}}{4} \mathrm{t}\) and \(\frac{\alpha^{2}}{4}\)
Motion in One Dimensions

141481 An object moves in a straight line with deceleration whose magnitude varies with velocity as \(3 \mathrm{v}^{2 / 3}\). If at an initial point, the velocity is \(8 \mathrm{~m} / \mathrm{s}\), then the distance travelled by the object before it stops is

1 \(2 \mathrm{~m}\)
2 \(4 \mathrm{~m}\)
3 \(6 \mathrm{~m}\)
4 \(8 \mathrm{~m}\)
Motion in One Dimensions

141479 The speed time graph of a particle moving along a fixed direction is shown. The distance travelled by the particle in \(10 \mathrm{~s}\) is
original image

1 \(20 \mathrm{~m}\)
2 \(30 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(60 \mathrm{~m}\)
Motion in One Dimensions

141477 Assertion : A body may be accelerated even when it is moving uniformly.
Reason: When direction of motion of the body is changing, the body must have acceleration.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Motion in One Dimensions

141480 Consider a particle moving along the positive direction of \(\mathrm{X}\)-axis. The velocity of the particle is given by \(v=\alpha \sqrt{x}\) ( \(\alpha\) is a positive constant). At time \(t=0\), if the particle is located at \(x=0\), the time dependence of the velocity and the acceleration of the particle are respectively

1 \(\frac{\alpha^{2}}{2}\) tand \(\frac{\alpha^{2}}{2}\)
2 \(\alpha^{2} t\) and \(\alpha^{2}\)
3 \(\frac{\alpha}{2} \mathrm{t}\) and \(\frac{\alpha}{2}\)
4 \(\frac{\alpha^{2}}{4} \mathrm{t}\) and \(\frac{\alpha^{2}}{4}\)
Motion in One Dimensions

141481 An object moves in a straight line with deceleration whose magnitude varies with velocity as \(3 \mathrm{v}^{2 / 3}\). If at an initial point, the velocity is \(8 \mathrm{~m} / \mathrm{s}\), then the distance travelled by the object before it stops is

1 \(2 \mathrm{~m}\)
2 \(4 \mathrm{~m}\)
3 \(6 \mathrm{~m}\)
4 \(8 \mathrm{~m}\)
Motion in One Dimensions

141479 The speed time graph of a particle moving along a fixed direction is shown. The distance travelled by the particle in \(10 \mathrm{~s}\) is
original image

1 \(20 \mathrm{~m}\)
2 \(30 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(60 \mathrm{~m}\)
Motion in One Dimensions

141477 Assertion : A body may be accelerated even when it is moving uniformly.
Reason: When direction of motion of the body is changing, the body must have acceleration.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Motion in One Dimensions

141480 Consider a particle moving along the positive direction of \(\mathrm{X}\)-axis. The velocity of the particle is given by \(v=\alpha \sqrt{x}\) ( \(\alpha\) is a positive constant). At time \(t=0\), if the particle is located at \(x=0\), the time dependence of the velocity and the acceleration of the particle are respectively

1 \(\frac{\alpha^{2}}{2}\) tand \(\frac{\alpha^{2}}{2}\)
2 \(\alpha^{2} t\) and \(\alpha^{2}\)
3 \(\frac{\alpha}{2} \mathrm{t}\) and \(\frac{\alpha}{2}\)
4 \(\frac{\alpha^{2}}{4} \mathrm{t}\) and \(\frac{\alpha^{2}}{4}\)
Motion in One Dimensions

141481 An object moves in a straight line with deceleration whose magnitude varies with velocity as \(3 \mathrm{v}^{2 / 3}\). If at an initial point, the velocity is \(8 \mathrm{~m} / \mathrm{s}\), then the distance travelled by the object before it stops is

1 \(2 \mathrm{~m}\)
2 \(4 \mathrm{~m}\)
3 \(6 \mathrm{~m}\)
4 \(8 \mathrm{~m}\)
Motion in One Dimensions

141479 The speed time graph of a particle moving along a fixed direction is shown. The distance travelled by the particle in \(10 \mathrm{~s}\) is
original image

1 \(20 \mathrm{~m}\)
2 \(30 \mathrm{~m}\)
3 \(40 \mathrm{~m}\)
4 \(60 \mathrm{~m}\)
Motion in One Dimensions

141477 Assertion : A body may be accelerated even when it is moving uniformly.
Reason: When direction of motion of the body is changing, the body must have acceleration.

1 If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 If Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
Motion in One Dimensions

141480 Consider a particle moving along the positive direction of \(\mathrm{X}\)-axis. The velocity of the particle is given by \(v=\alpha \sqrt{x}\) ( \(\alpha\) is a positive constant). At time \(t=0\), if the particle is located at \(x=0\), the time dependence of the velocity and the acceleration of the particle are respectively

1 \(\frac{\alpha^{2}}{2}\) tand \(\frac{\alpha^{2}}{2}\)
2 \(\alpha^{2} t\) and \(\alpha^{2}\)
3 \(\frac{\alpha}{2} \mathrm{t}\) and \(\frac{\alpha}{2}\)
4 \(\frac{\alpha^{2}}{4} \mathrm{t}\) and \(\frac{\alpha^{2}}{4}\)
Motion in One Dimensions

141481 An object moves in a straight line with deceleration whose magnitude varies with velocity as \(3 \mathrm{v}^{2 / 3}\). If at an initial point, the velocity is \(8 \mathrm{~m} / \mathrm{s}\), then the distance travelled by the object before it stops is

1 \(2 \mathrm{~m}\)
2 \(4 \mathrm{~m}\)
3 \(6 \mathrm{~m}\)
4 \(8 \mathrm{~m}\)