Instantaneous Velocity and Instantaneous Speed
PHXI03:MOTION IN A STRAIGHT LINE

362267 Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \({x_P}(t) = at + b{t^2}\) and \({x_Q}(t) = ft - {t^2}.\) At what time do the cars have the same velocity?

1 \(\frac{{a - f}}{{1 + b}}\)
2 \(\frac{{a + f}}{{2(b - 1)}}\)
3 \(\frac{{a + f}}{{2(1 + b)}}\)
4 \(\frac{{f - a}}{{2(1 + b)}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by \(x=\left(5 t^{2}-4 t+5\right) m\). The magnitude of velocity of the particle at \(t=2 s\) will be

1 \(10\;m{s^{ - 1}}\)
2 \(14\;m{s^{ - 1}}\)
3 \(16\;m{s^{ - 1}}\)
4 \(0.6\;m{s^{ - 1}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362269 A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.
supporting img

1 \(C\)
2 \(B\)
3 \(D\)
4 \(A\)
PHXI03:MOTION IN A STRAIGHT LINE

362270 Statement A :
The average and instanteneous velocities have same value in a uniform motion.
Statement B :
In uniform motion, the velocity of an object increases uniformly.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362271 The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure.
(A) \(A\) lives closer to the school
(B) \(B\) lives closer to the school
(C) \(A\) takes lesser time to reach home
(D) \(A\) travels faster than \(B\)
(E) \(B\) travels faster than \(A\).
supporting img
Choose the correct answer from the option given below:

1 (A), (C) and (D) only
2 (A), (C) and (E) only
3 (B) and (E) only
4 (A) and (E) only.
PHXI03:MOTION IN A STRAIGHT LINE

362267 Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \({x_P}(t) = at + b{t^2}\) and \({x_Q}(t) = ft - {t^2}.\) At what time do the cars have the same velocity?

1 \(\frac{{a - f}}{{1 + b}}\)
2 \(\frac{{a + f}}{{2(b - 1)}}\)
3 \(\frac{{a + f}}{{2(1 + b)}}\)
4 \(\frac{{f - a}}{{2(1 + b)}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by \(x=\left(5 t^{2}-4 t+5\right) m\). The magnitude of velocity of the particle at \(t=2 s\) will be

1 \(10\;m{s^{ - 1}}\)
2 \(14\;m{s^{ - 1}}\)
3 \(16\;m{s^{ - 1}}\)
4 \(0.6\;m{s^{ - 1}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362269 A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.
supporting img

1 \(C\)
2 \(B\)
3 \(D\)
4 \(A\)
PHXI03:MOTION IN A STRAIGHT LINE

362270 Statement A :
The average and instanteneous velocities have same value in a uniform motion.
Statement B :
In uniform motion, the velocity of an object increases uniformly.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362271 The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure.
(A) \(A\) lives closer to the school
(B) \(B\) lives closer to the school
(C) \(A\) takes lesser time to reach home
(D) \(A\) travels faster than \(B\)
(E) \(B\) travels faster than \(A\).
supporting img
Choose the correct answer from the option given below:

1 (A), (C) and (D) only
2 (A), (C) and (E) only
3 (B) and (E) only
4 (A) and (E) only.
PHXI03:MOTION IN A STRAIGHT LINE

362267 Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \({x_P}(t) = at + b{t^2}\) and \({x_Q}(t) = ft - {t^2}.\) At what time do the cars have the same velocity?

1 \(\frac{{a - f}}{{1 + b}}\)
2 \(\frac{{a + f}}{{2(b - 1)}}\)
3 \(\frac{{a + f}}{{2(1 + b)}}\)
4 \(\frac{{f - a}}{{2(1 + b)}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by \(x=\left(5 t^{2}-4 t+5\right) m\). The magnitude of velocity of the particle at \(t=2 s\) will be

1 \(10\;m{s^{ - 1}}\)
2 \(14\;m{s^{ - 1}}\)
3 \(16\;m{s^{ - 1}}\)
4 \(0.6\;m{s^{ - 1}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362269 A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.
supporting img

1 \(C\)
2 \(B\)
3 \(D\)
4 \(A\)
PHXI03:MOTION IN A STRAIGHT LINE

362270 Statement A :
The average and instanteneous velocities have same value in a uniform motion.
Statement B :
In uniform motion, the velocity of an object increases uniformly.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362271 The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure.
(A) \(A\) lives closer to the school
(B) \(B\) lives closer to the school
(C) \(A\) takes lesser time to reach home
(D) \(A\) travels faster than \(B\)
(E) \(B\) travels faster than \(A\).
supporting img
Choose the correct answer from the option given below:

1 (A), (C) and (D) only
2 (A), (C) and (E) only
3 (B) and (E) only
4 (A) and (E) only.
PHXI03:MOTION IN A STRAIGHT LINE

362267 Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \({x_P}(t) = at + b{t^2}\) and \({x_Q}(t) = ft - {t^2}.\) At what time do the cars have the same velocity?

1 \(\frac{{a - f}}{{1 + b}}\)
2 \(\frac{{a + f}}{{2(b - 1)}}\)
3 \(\frac{{a + f}}{{2(1 + b)}}\)
4 \(\frac{{f - a}}{{2(1 + b)}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by \(x=\left(5 t^{2}-4 t+5\right) m\). The magnitude of velocity of the particle at \(t=2 s\) will be

1 \(10\;m{s^{ - 1}}\)
2 \(14\;m{s^{ - 1}}\)
3 \(16\;m{s^{ - 1}}\)
4 \(0.6\;m{s^{ - 1}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362269 A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.
supporting img

1 \(C\)
2 \(B\)
3 \(D\)
4 \(A\)
PHXI03:MOTION IN A STRAIGHT LINE

362270 Statement A :
The average and instanteneous velocities have same value in a uniform motion.
Statement B :
In uniform motion, the velocity of an object increases uniformly.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362271 The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure.
(A) \(A\) lives closer to the school
(B) \(B\) lives closer to the school
(C) \(A\) takes lesser time to reach home
(D) \(A\) travels faster than \(B\)
(E) \(B\) travels faster than \(A\).
supporting img
Choose the correct answer from the option given below:

1 (A), (C) and (D) only
2 (A), (C) and (E) only
3 (B) and (E) only
4 (A) and (E) only.
PHXI03:MOTION IN A STRAIGHT LINE

362267 Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \({x_P}(t) = at + b{t^2}\) and \({x_Q}(t) = ft - {t^2}.\) At what time do the cars have the same velocity?

1 \(\frac{{a - f}}{{1 + b}}\)
2 \(\frac{{a + f}}{{2(b - 1)}}\)
3 \(\frac{{a + f}}{{2(1 + b)}}\)
4 \(\frac{{f - a}}{{2(1 + b)}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by \(x=\left(5 t^{2}-4 t+5\right) m\). The magnitude of velocity of the particle at \(t=2 s\) will be

1 \(10\;m{s^{ - 1}}\)
2 \(14\;m{s^{ - 1}}\)
3 \(16\;m{s^{ - 1}}\)
4 \(0.6\;m{s^{ - 1}}\)
PHXI03:MOTION IN A STRAIGHT LINE

362269 A particle shows distance-time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point.
supporting img

1 \(C\)
2 \(B\)
3 \(D\)
4 \(A\)
PHXI03:MOTION IN A STRAIGHT LINE

362270 Statement A :
The average and instanteneous velocities have same value in a uniform motion.
Statement B :
In uniform motion, the velocity of an object increases uniformly.

1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
PHXI03:MOTION IN A STRAIGHT LINE

362271 The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure.
(A) \(A\) lives closer to the school
(B) \(B\) lives closer to the school
(C) \(A\) takes lesser time to reach home
(D) \(A\) travels faster than \(B\)
(E) \(B\) travels faster than \(A\).
supporting img
Choose the correct answer from the option given below:

1 (A), (C) and (D) only
2 (A), (C) and (E) only
3 (B) and (E) only
4 (A) and (E) only.