A particle moves in space such that:
\(x=2t^3+3t+4;~y=t^2+4t-1;~z=2sin\pi t\)
where \(x,~y,~z\)  are measured in meters and \(t\) in seconds. The acceleration of the particle at \(t=3\) seconds will be:

1. \(36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\hat{\mathrm{k}} \) ms-2
2. \(36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\pi \hat{\mathrm{k}} \) ms-2
3. \(36 \hat{\mathrm{i}}+2 \hat{\mathrm{j}} \) ms-2
4. \(12 \hat{\mathrm{i}}+2 \hat{\mathrm{j}} \) ms-2

Subtopic:  Acceleration |
 67%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A ship \(A\) is moving westward with a speed of \(10\) kmph and a ship \(B\), \(100 ~\text{km}\) South of \(A\), is moving northward with a speed of \(10\) \(\text{kmph}\). The time after which the distance between them becomes the shortest is:
1. \(0\) h
2. \(5\) h
3. \(5\sqrt{2}\) h
4. \(10\sqrt{2}\) h

Subtopic:  Relative Motion |
 50%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A projectile is fired from the surface of the earth with a velocity of \(5\) ms–1 and at an angle \(\theta\) with the horizontal. Another projectile fired from another planet with a velocity of \(3\) ms–1 at the same angle follows a trajectory that is identical to the trajectory of the projectile fired from the Earth. The value of the acceleration due to gravity on the other planet is: (given \(g=9.8\) ms–2)
1. \(3.5\) m/s2
2. \(5.9\) m/s2
3. \(16.3\) m/s2
4. \(110.8\) m/s2

Subtopic:  Projectile Motion |
 71%
From NCERT
AIPMT - 2014
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The velocity of a projectile at the initial point \(A\) is \(2\hat i+3\hat j~\)m/s. Its velocity (in m/s) at point \(B\) is:
              

1. \(-2\hat i+3\hat j~\) 2. \(2\hat i-3\hat j~\)
3. \(2\hat i+3\hat j~\) 4. \(-2\hat i-3\hat j~\)
Subtopic:  Projectile Motion |
 84%
From NCERT
AIPMT - 2013
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is:
1. θ=tan-114
2. θ=tan-14
3. θ=tan-12
4. θ=450

Subtopic:  Projectile Motion |
 75%
From NCERT
AIPMT - 2012
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A particle moves in a circle of radius \(5\) cm with constant speed and time period \(0.2\pi\) s. The acceleration of the particle is:

1. \(25\) m/s2 2. \(36\) m/s2
3. \(5\) m/s2 4. \(15\) m/s2
Subtopic:  Circular Motion |
 80%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A body is moving with a velocity of \(30\) m/s towards the east. After \(10\) s, its velocity becomes \(40\) m/s towards the north. The average acceleration of the body is:
1. \( 7 \mathrm{~m} / \mathrm{s}^2 \)
2. \( \sqrt{7} \mathrm{~m} / \mathrm{s}^2 \)
3. \( 5 \mathrm{~m} / \mathrm{s}^2 \)
4. \( 1 \mathrm{~m} / \mathrm{s}^2\)

Subtopic:  Acceleration |
 76%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A missile is fired for a maximum range with an initial velocity of 20 m/s. If g= 10 m/s2, then the range of the missile will be:
1. 50 m
2. 60 m
3. 20 m
4. 40 m

Subtopic:  Projectile Motion |
 83%
From NCERT
AIPMT - 2011
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A particle starting from the origin \((0,0)\) moves in a straight line in the \((x,y)\) plane. Its coordinates at a later time are (3, \(3\)). The path of the particle makes an angle of __________ with the x-axis:
1. \(30^\circ\)
2. \(45^\circ\)
3. \(60^\circ\)
4. \(0\)

Subtopic:  Position & Displacement |
 76%
From NCERT
AIPMT - 2007
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

For a projectile projected at angles (45°-θ) and (45°+θ), the horizontal ranges described by the projectile are in the ratio of:
1. 1:1
2. 2:3
3. 1:2
4. 2:1

Subtopic:  Projectile Motion |
 87%
From NCERT
AIPMT - 2006
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh