00. Distance and Displacement
Motion in One Dimensions

141183 A car travelled half the distance with a velocity ' \(v\) ' and it covered the remaining half distance with a velocity \(\left(\frac{v}{2}\right)\) in the first half time and with velocity ' \(2 v\) ' in the second half time. The average velocity of the car for the whole journey is

1 \(\frac{10 \mathrm{v}}{14}\)
2 \(\frac{10 \mathrm{v}}{9}\)
3 \(\frac{7 v}{4}\)
4 \(\frac{10 \mathrm{v}}{7}\)
Motion in One Dimensions

141184 The relationship between the final velocity \(v\) and the distance \(x\) travelled by a bus moving with uniform acceleration is \(v=\sqrt{256-10 x}\). The acceleration of the bus is (All quantities are given in SI units)

1 \(-5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(-10 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-20 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-15 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141185 A particle moves in a straight line with uniform acceleration and with initial velocity of \(2 \mathrm{~m} / \mathrm{s}\). Its average velocity after moving for \(4 \mathrm{~s}\) is \(6 \mathrm{~m} / \mathrm{s}\). The acceleration of the particle.

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

141186 A particle is moving along \(x\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x\) \(=0\). The displacement of the particle as function of time is

1 \(e^{-\beta t}\)
2 \(\frac{1}{\beta} \mathrm{e}^{(1-\beta \mathrm{t})}\)
3 \(\frac{1}{\beta} \log [1-\beta \mathrm{t}]\)
4 \(\frac{1}{\beta} \log [1+\beta \mathrm{t}]\)
Motion in One Dimensions

141187 The velocity of a particle is only a function of its position \(v(x)=e^{-x}\). The position of the particle at time \(t=0\) is \(x=0\). The displacement of the particle varies with time as

1 \(e^{t}\)
2 \(\mathrm{e}^{(1-\mathrm{t})}\)
3 \(\ln (\mathrm{t})\)
4 \(\ln (1+t)\)
Motion in One Dimensions

141183 A car travelled half the distance with a velocity ' \(v\) ' and it covered the remaining half distance with a velocity \(\left(\frac{v}{2}\right)\) in the first half time and with velocity ' \(2 v\) ' in the second half time. The average velocity of the car for the whole journey is

1 \(\frac{10 \mathrm{v}}{14}\)
2 \(\frac{10 \mathrm{v}}{9}\)
3 \(\frac{7 v}{4}\)
4 \(\frac{10 \mathrm{v}}{7}\)
Motion in One Dimensions

141184 The relationship between the final velocity \(v\) and the distance \(x\) travelled by a bus moving with uniform acceleration is \(v=\sqrt{256-10 x}\). The acceleration of the bus is (All quantities are given in SI units)

1 \(-5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(-10 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-20 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-15 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141185 A particle moves in a straight line with uniform acceleration and with initial velocity of \(2 \mathrm{~m} / \mathrm{s}\). Its average velocity after moving for \(4 \mathrm{~s}\) is \(6 \mathrm{~m} / \mathrm{s}\). The acceleration of the particle.

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

141186 A particle is moving along \(x\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x\) \(=0\). The displacement of the particle as function of time is

1 \(e^{-\beta t}\)
2 \(\frac{1}{\beta} \mathrm{e}^{(1-\beta \mathrm{t})}\)
3 \(\frac{1}{\beta} \log [1-\beta \mathrm{t}]\)
4 \(\frac{1}{\beta} \log [1+\beta \mathrm{t}]\)
Motion in One Dimensions

141187 The velocity of a particle is only a function of its position \(v(x)=e^{-x}\). The position of the particle at time \(t=0\) is \(x=0\). The displacement of the particle varies with time as

1 \(e^{t}\)
2 \(\mathrm{e}^{(1-\mathrm{t})}\)
3 \(\ln (\mathrm{t})\)
4 \(\ln (1+t)\)
Motion in One Dimensions

141183 A car travelled half the distance with a velocity ' \(v\) ' and it covered the remaining half distance with a velocity \(\left(\frac{v}{2}\right)\) in the first half time and with velocity ' \(2 v\) ' in the second half time. The average velocity of the car for the whole journey is

1 \(\frac{10 \mathrm{v}}{14}\)
2 \(\frac{10 \mathrm{v}}{9}\)
3 \(\frac{7 v}{4}\)
4 \(\frac{10 \mathrm{v}}{7}\)
Motion in One Dimensions

141184 The relationship between the final velocity \(v\) and the distance \(x\) travelled by a bus moving with uniform acceleration is \(v=\sqrt{256-10 x}\). The acceleration of the bus is (All quantities are given in SI units)

1 \(-5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(-10 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-20 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-15 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141185 A particle moves in a straight line with uniform acceleration and with initial velocity of \(2 \mathrm{~m} / \mathrm{s}\). Its average velocity after moving for \(4 \mathrm{~s}\) is \(6 \mathrm{~m} / \mathrm{s}\). The acceleration of the particle.

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

141186 A particle is moving along \(x\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x\) \(=0\). The displacement of the particle as function of time is

1 \(e^{-\beta t}\)
2 \(\frac{1}{\beta} \mathrm{e}^{(1-\beta \mathrm{t})}\)
3 \(\frac{1}{\beta} \log [1-\beta \mathrm{t}]\)
4 \(\frac{1}{\beta} \log [1+\beta \mathrm{t}]\)
Motion in One Dimensions

141187 The velocity of a particle is only a function of its position \(v(x)=e^{-x}\). The position of the particle at time \(t=0\) is \(x=0\). The displacement of the particle varies with time as

1 \(e^{t}\)
2 \(\mathrm{e}^{(1-\mathrm{t})}\)
3 \(\ln (\mathrm{t})\)
4 \(\ln (1+t)\)
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Motion in One Dimensions

141183 A car travelled half the distance with a velocity ' \(v\) ' and it covered the remaining half distance with a velocity \(\left(\frac{v}{2}\right)\) in the first half time and with velocity ' \(2 v\) ' in the second half time. The average velocity of the car for the whole journey is

1 \(\frac{10 \mathrm{v}}{14}\)
2 \(\frac{10 \mathrm{v}}{9}\)
3 \(\frac{7 v}{4}\)
4 \(\frac{10 \mathrm{v}}{7}\)
Motion in One Dimensions

141184 The relationship between the final velocity \(v\) and the distance \(x\) travelled by a bus moving with uniform acceleration is \(v=\sqrt{256-10 x}\). The acceleration of the bus is (All quantities are given in SI units)

1 \(-5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(-10 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-20 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-15 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141185 A particle moves in a straight line with uniform acceleration and with initial velocity of \(2 \mathrm{~m} / \mathrm{s}\). Its average velocity after moving for \(4 \mathrm{~s}\) is \(6 \mathrm{~m} / \mathrm{s}\). The acceleration of the particle.

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

141186 A particle is moving along \(x\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x\) \(=0\). The displacement of the particle as function of time is

1 \(e^{-\beta t}\)
2 \(\frac{1}{\beta} \mathrm{e}^{(1-\beta \mathrm{t})}\)
3 \(\frac{1}{\beta} \log [1-\beta \mathrm{t}]\)
4 \(\frac{1}{\beta} \log [1+\beta \mathrm{t}]\)
Motion in One Dimensions

141187 The velocity of a particle is only a function of its position \(v(x)=e^{-x}\). The position of the particle at time \(t=0\) is \(x=0\). The displacement of the particle varies with time as

1 \(e^{t}\)
2 \(\mathrm{e}^{(1-\mathrm{t})}\)
3 \(\ln (\mathrm{t})\)
4 \(\ln (1+t)\)
Motion in One Dimensions

141183 A car travelled half the distance with a velocity ' \(v\) ' and it covered the remaining half distance with a velocity \(\left(\frac{v}{2}\right)\) in the first half time and with velocity ' \(2 v\) ' in the second half time. The average velocity of the car for the whole journey is

1 \(\frac{10 \mathrm{v}}{14}\)
2 \(\frac{10 \mathrm{v}}{9}\)
3 \(\frac{7 v}{4}\)
4 \(\frac{10 \mathrm{v}}{7}\)
Motion in One Dimensions

141184 The relationship between the final velocity \(v\) and the distance \(x\) travelled by a bus moving with uniform acceleration is \(v=\sqrt{256-10 x}\). The acceleration of the bus is (All quantities are given in SI units)

1 \(-5 \mathrm{~m} / \mathrm{s}^{2}\)
2 \(-10 \mathrm{~m} / \mathrm{s}^{2}\)
3 \(-20 \mathrm{~m} / \mathrm{s}^{2}\)
4 \(-15 \mathrm{~m} / \mathrm{s}^{2}\)
Motion in One Dimensions

141185 A particle moves in a straight line with uniform acceleration and with initial velocity of \(2 \mathrm{~m} / \mathrm{s}\). Its average velocity after moving for \(4 \mathrm{~s}\) is \(6 \mathrm{~m} / \mathrm{s}\). The acceleration of the particle.

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

141186 A particle is moving along \(x\)-axis with velocity \(v=e^{-\beta x}\). At time \(t=0\), the particle is located at \(x\) \(=0\). The displacement of the particle as function of time is

1 \(e^{-\beta t}\)
2 \(\frac{1}{\beta} \mathrm{e}^{(1-\beta \mathrm{t})}\)
3 \(\frac{1}{\beta} \log [1-\beta \mathrm{t}]\)
4 \(\frac{1}{\beta} \log [1+\beta \mathrm{t}]\)
Motion in One Dimensions

141187 The velocity of a particle is only a function of its position \(v(x)=e^{-x}\). The position of the particle at time \(t=0\) is \(x=0\). The displacement of the particle varies with time as

1 \(e^{t}\)
2 \(\mathrm{e}^{(1-\mathrm{t})}\)
3 \(\ln (\mathrm{t})\)
4 \(\ln (1+t)\)