# A particle moves along a straight line and its position as a function of time is given by$\mathrm{}$ $$x= t^3-3t^2+3t+3$$ then particle: 1.  stops at $$t=1~\text{s}$$ and reverses its direction of motion. 2.  stops at $$t= 1~\text{s}$$ and continues further without a change of direction. 3.  stops at $$t=2~\text{s}$$ and reverses its direction of motion. 4.  stops at $$t=2~\text{s}$$ and continues further without a change of direction.

Subtopic:  Instantaneous Speed & Instantaneous Velocity |
51%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

If the velocity of a particle is $$v=At+Bt^{2},$$ where $$A$$ and $$B$$ are constants, then the distance travelled by it between $$1~\text{s}$$ and $$2~\text{s}$$ is:

 1 $$3A+7B$$ 2 $$\frac{3}{2}A+\frac{7}{3}B$$ 3 $$\frac{A}{2}+\frac{B}{3}$$ 4 $$\frac{3A}{2}+4B$$
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
88%
From NCERT
NEET - 2016
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A particle of unit mass undergoes one-dimensional motion such that its velocity varies according to $$v(x)= βx^{- 2 n}$$ where $$\beta$$ and $$n$$ are constants and $$x$$ is the position of the particle. The acceleration of the particle as a function of $$x$$ is given by:
1. $$- 2 nβ^{2} x^{- 2 n - 1}$$
2. $$- 2 nβ^{2} x^{- 4 n - 1}$$
3. $$- 2 \beta^{2} x^{- 2 n + 1}$$
4. $$- 2 nβ^{2} x^{- 4 n + 1}$$
${}^{}$

Subtopic:  Non Uniform Acceleration |
68%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A stone falls freely under gravity. It covers distances $$h_1,~h_2$$ and $$h_3$$ in the first $$5$$ seconds, the next $$5$$ seconds and the next $$5$$ seconds respectively. The relation between $$h_1,~h_2$$ and $$h_3$$ is:

 1 $$h_1=\frac{h_2}{3}=\frac{h_3}{5}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \$$ 2 $$h_2=3h_1$$ and $$h_3=3h_2$$ 3 $$h_1=h_2=h_3$$ 4 $$h_1=2h_2=3h_3$$
Subtopic:  Uniformly Accelerated Motion |
82%
From NCERT
AIPMT - 2013
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A ball is dropped from a high-rise platform at $$t=0$$ starting from rest. After $$6$$ seconds, another ball is thrown downwards from the same platform with speed $$v$$. The two balls meet after $$18$$ seconds. What is the value of $$v$$?

 1 $$75$$ ms-1 2 $$55$$ ms-1 3 $$40$$ ms-1 4 $$60$$ ms-1
Subtopic:  Uniformly Accelerated Motion |
59%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A particle moves in a straight line with a constant acceleration. It changes its velocity from $$10$$ ms-1 to $$20$$ ms-1 while covering a distance of $$135$$ m in $$t$$ seconds. The value of $$t$$ is:

 1 $$10$$ 2 $$1.8$$ 3 $$12$$ 4 $$9$$
Subtopic:  Uniformly Accelerated Motion |
78%
From NCERT
AIPMT - 2008
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A car moves from $$X$$ to $$Y$$ with a uniform speed $$v_u$$ and returns to $$X$$ with a uniform speed $$v_d.$$ The average speed for this round trip is:

 1 $$\frac{2 v_{d} v_{u}}{v_{d} + v_{u}}$$ 2 $$\sqrt{v_{u} v_{d}}$$ 3 $$\frac{v_{d} v_{u}}{v_{d} + v_{u}}$$ 4 $$\frac{v_{u} + v_{d}}{2}$$
Subtopic:  Average Speed & Average Velocity |
82%
From NCERT
AIPMT - 2007
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A particle moves along a straight line OX. At a time $$t$$ (in seconds), the displacement $$x$$ (in metres) of the particle from O is given by $$x= 40 +12t-t^3$$. How long would the particle travel before coming to rest?

 1 $$24$$ m 2 $$40$$ m 3 $$56$$ m 4 $$16$$ m
Subtopic:  Instantaneous Speed & Instantaneous Velocity |
From NCERT
AIPMT - 2006
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A ball is dropped vertically from a height $$h$$ above the ground. It hits the ground and bounces up vertically to a height of $$\frac{h}{2}$$. Neglecting subsequent motion and air resistance, its velocity $$v$$ varies with the height $$h$$ as:
[Take vertically upwards direction as positive.]

 1 2 3 4
Subtopic:  Graphs |
51%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints
To view explanation, please take trial in the course.
NEET 2025 - Target Batch

A car $$A$$ is traveling on a straight level road at a uniform speed of $$60$$ km/h. It is followed by another car $$B$$ which is moving at a speed of $$70$$ km/h. When the distance between them is $$2.5$$ km, car $$B$$ is given a deceleration of $$20$$ km/h2. After how much time will car $$B$$ catch up with car $$A$$?
1. $$1$$ hr
2. $$\frac{1}{2}$$ hr
3. $$\frac{1}{4}$$ hr
4. $$\frac{1}{8}$$ hr

Subtopic:  Relative Motion in One Dimension |
65%
From NCERT
To view explanation, please take trial in the course.
NEET 2025 - Target Batch
Hints