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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 $x_{P} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2} .$ 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)}

Explanation:

$\frac{d x_{p}}{d t} = a + 2 b t$
$\frac{d x_{q}}{d t} = f - 2 t$
$a + 2 b t = f - 2 t$
$t = \frac{f - a}{(2 b + 2)}$

NEET - 2016

PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by $x = (5 t^{2} - 4 t + 5) m$ . 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}

Explanation:

$x = 5 t^{2} - 4 t + 5$
$v = \frac{d x}{d t} = (10 t - 4) m / s$
At $t = 2$ sec
$v_{t = 2} = 10 \times 2 - 4 = 16 m / s$

JEE - 2023

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

Explanation:

Maximum velocity point means, the point at which slope is maximum at point $C$ , slope is maximum.

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.

Explanation:

As the slope of $x - t$ graph gives speed and slope of $B$ is more than slope of $A$ .
supporting img
Thus, the speed of $B$ is more than $A$ .
As $x_{1} < x_{2}$ , so $A$ lives closer to school.
Hence, option $A$ and $E$ are correct.

JEE - 2023

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 $x_{P} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2} .$ 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)}

Explanation:

$\frac{d x_{p}}{d t} = a + 2 b t$
$\frac{d x_{q}}{d t} = f - 2 t$
$a + 2 b t = f - 2 t$
$t = \frac{f - a}{(2 b + 2)}$

NEET - 2016

PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by $x = (5 t^{2} - 4 t + 5) m$ . 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}

Explanation:

$x = 5 t^{2} - 4 t + 5$
$v = \frac{d x}{d t} = (10 t - 4) m / s$
At $t = 2$ sec
$v_{t = 2} = 10 \times 2 - 4 = 16 m / s$

JEE - 2023

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

Explanation:

Maximum velocity point means, the point at which slope is maximum at point $C$ , slope is maximum.

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.

Explanation:

As the slope of $x - t$ graph gives speed and slope of $B$ is more than slope of $A$ .
supporting img
Thus, the speed of $B$ is more than $A$ .
As $x_{1} < x_{2}$ , so $A$ lives closer to school.
Hence, option $A$ and $E$ are correct.

JEE - 2023

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 $x_{P} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2} .$ 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)}

Explanation:

$\frac{d x_{p}}{d t} = a + 2 b t$
$\frac{d x_{q}}{d t} = f - 2 t$
$a + 2 b t = f - 2 t$
$t = \frac{f - a}{(2 b + 2)}$

NEET - 2016

PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by $x = (5 t^{2} - 4 t + 5) m$ . 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}

Explanation:

$x = 5 t^{2} - 4 t + 5$
$v = \frac{d x}{d t} = (10 t - 4) m / s$
At $t = 2$ sec
$v_{t = 2} = 10 \times 2 - 4 = 16 m / s$

JEE - 2023

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

Explanation:

Maximum velocity point means, the point at which slope is maximum at point $C$ , slope is maximum.

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.

Explanation:

As the slope of $x - t$ graph gives speed and slope of $B$ is more than slope of $A$ .
supporting img
Thus, the speed of $B$ is more than $A$ .
As $x_{1} < x_{2}$ , so $A$ lives closer to school.
Hence, option $A$ and $E$ are correct.

JEE - 2023

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 $x_{P} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2} .$ 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)}

Explanation:

$\frac{d x_{p}}{d t} = a + 2 b t$
$\frac{d x_{q}}{d t} = f - 2 t$
$a + 2 b t = f - 2 t$
$t = \frac{f - a}{(2 b + 2)}$

NEET - 2016

PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by $x = (5 t^{2} - 4 t + 5) m$ . 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}

Explanation:

$x = 5 t^{2} - 4 t + 5$
$v = \frac{d x}{d t} = (10 t - 4) m / s$
At $t = 2$ sec
$v_{t = 2} = 10 \times 2 - 4 = 16 m / s$

JEE - 2023

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

Explanation:

Maximum velocity point means, the point at which slope is maximum at point $C$ , slope is maximum.

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.

Explanation:

As the slope of $x - t$ graph gives speed and slope of $B$ is more than slope of $A$ .
supporting img
Thus, the speed of $B$ is more than $A$ .
As $x_{1} < x_{2}$ , so $A$ lives closer to school.
Hence, option $A$ and $E$ are correct.

JEE - 2023

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 $x_{P} (t) = a t + b t^{2}$ and $x_{Q} (t) = f t - t^{2} .$ 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)}

Explanation:

$\frac{d x_{p}}{d t} = a + 2 b t$
$\frac{d x_{q}}{d t} = f - 2 t$
$a + 2 b t = f - 2 t$
$t = \frac{f - a}{(2 b + 2)}$

NEET - 2016

PHXI03:MOTION IN A STRAIGHT LINE

362268 The position of a particle related to time is given by $x = (5 t^{2} - 4 t + 5) m$ . 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}

Explanation:

$x = 5 t^{2} - 4 t + 5$
$v = \frac{d x}{d t} = (10 t - 4) m / s$
At $t = 2$ sec
$v_{t = 2} = 10 \times 2 - 4 = 16 m / s$

JEE - 2023

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

Explanation:

Maximum velocity point means, the point at which slope is maximum at point $C$ , slope is maximum.

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.

Explanation:

As the slope of $x - t$ graph gives speed and slope of $B$ is more than slope of $A$ .
supporting img
Thus, the speed of $B$ is more than $A$ .
As $x_{1} < x_{2}$ , so $A$ lives closer to school.
Hence, option $A$ and $E$ are correct.

JEE - 2023