Motion in a Straight Line

A gas balloon is going up with a constant velocity of $10 \mathrm{~m} / \mathrm{s}$. When this balloon reached a height of 75 m , a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when ...

From 18 m height above the ground a ball is dropped from rest . The height above the ground at which the magnitude of velocity equal to the magnitude of acceleration (in the same set of units) due to gravity is $\_\_\_\_$ m.
(Take $g=10 \ma...

The velocity $(v)$ versus time $(t)$ plot of a particle is shown in the figure, for a time interval of 40 s . The total distance travelled by the particle and the average velocity during this period are, respectively
$\_\_\_\_$.

Two cars $A$ and $B$ are moving in the same direction along a straight line with speeds $100 \mathrm{~km} / \mathrm{h}$ and $80 \mathrm{~km} / \mathrm{h}$, respectively such that car $A$ is moving ahead of car $B$. A person in car $B$ throw...

Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the sixth drop begins to fall. The height at which the fourth drop will be from ground, at the instant when the first d...

A particle starts moving from time $t=0$ and its coordinate is given as $x(t) = 4t^3 - 3t$
A. The particle returns to its original position (origin) 0.866 units later
B. The particle is 1 unit away from origin at its turning point
C. Accele...

The velocity $(v)$ - Distance $(x)$ graph is shown in figure. Which graph represents acceleration(a) versus distance ( $x$ ) variation of this system?

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts deaccelerating with $3 \mathrm{~m} / \mathrm{s}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratroo...

The displacement x versus time graph is shown below.

(A) The average velocity during 0 to 3 s is $10 \mathrm{~m} / \mathrm{s}$
(B) The average velocity during 3 to 5 s is $0 \mathrm{~m} / \mathrm{s}$
(C) The instantaneous velocity at $\mat...

\(\text {Which of the following curves possibly represent one-dimensional motion of a particle? }\)

Choose the correct answer from the options given below :

A particle moves along the $x$-axis and has its displacement $x$ varying with time t according to the equation:
\(x=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2\)
where $\mathrm{c}_0$ and c are constants of appropria...

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\frac{3}{2} x$ distance. The average velocity in this motion is $\frac{50}{7} \mathrm{~m} / \mathr...

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum poss...

The velocity-time graph of an object moving along a straight line is shown in the figure. What is the distance covered by the object between $t = 0$ to $t = 4s$?

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is ̱_______ km .

A particle moving in a straight line covers half the distance with speed \(6 \mathrm{~m} / \mathrm{s}\). The other half is covered in two equal time intervals with speeds \(9 \mathrm{~m} / \mathrm{s}\) and \(15 \mathrm{~m} / \mathrm{s}\) re...

Two cars are travelling towards each other at speed of \(20 \mathrm{~m} \mathrm{~s}^{-1}\) each. When the cars are \(300 \mathrm{~m}\) apart, both the drivers apply brakes and the cars retard at the rate of $$2 \mathrm{~m} \mathrm{~s}^{-2}$...

A train starting from rest first accelerates uniformly up to a speed of \(80 \mathrm{~km} / \mathrm{h}\) for time \(t\), then it moves with a constant speed for time \(3 t\). The average speed of the train for this duration of journey will ...

A particle moves in a straight line so that its displacement \(x\) at any time \(t\) is given by \(x^2=1+t^2\). Its acceleration at any time \(\mathrm{t}\) is \(x^{-\mathrm{n}}\) where \(\mathrm{n}=\) _________.

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in \(t_1\). If it is projected vertically downwards from the same point with the same speed, it reaches the ground in \(t_2\). Time required...

A body moves on a frictionless plane starting from rest. If \(\mathrm{S_n}\) is distance moved between \(\mathrm{t=n-1}\) and \(\mathrm{t}=\mathrm{n}\) and \(\mathrm{S}_{\mathrm{n}-1}\) is distance moved between \(\mathrm{t}=\mathrm{n}-2\) ...

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((\mathrm{n}+2)^{\text {th }}\) second. The acceleration is :

A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 s\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ____...

The relation between time '\(t\)' and distance '\(x\)' is \(t=\alpha x^2+\beta x\), where \(\alpha\) and \(\beta\) are constants. The relation between acceleration \((a)\) and velocity \((v)\) is :

The displacement and the increase in the velocity of a moving particle in the time interval of \(t\) to \((t+1) \mathrm{s}\) are \(125 \mathrm{~m}\) and \(50 \mathrm{~m} / \mathrm{s}\), respectively. The distance travelled by the particle i...

A body starts moving from rest with constant acceleration covers displacement \(S_1\) in first \((p-1)\) seconds and \(\mathrm{S}_2\) in first \(p\) seconds. The displacement \(\mathrm{S}_1+\mathrm{S}_2\) will be made in time :

A particle is moving in a straight line. The variation of position '\(x\)' as a function of time '\(t\)' is given as \(x=\left(t^3-6 t^2+20 t+15\right) m\). The velocity of the body when its acceleration becomes zero is :

A body falling under gravity covers two points \(A\) and \(B\) separated by \(80 \mathrm{~m}\) in \(2 \mathrm{~s}\). The distance of upper point A from the starting point is _________ \(\mathrm{m}\) (use \(\mathrm{g}=10 \mathrm{~ms}^{-2}\))...

A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$,...

A particle initially at rest starts moving from reference point $x=0$ along $x$-axis, with velocity $v$ that varies as $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The acceleration of the particle is __________ $\mathrm{ms}^{-2}$.

Train A is moving along two parallel rail tracks towards north with speed \(72 \mathrm{~km} / \mathrm{h}\) and train B is moving towards south with speed \(108 \mathrm{~km} / \mathrm{h}\). Velocity of train B with respect to A and velocity ...

Given below are two statements
Statement I : Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement II : Area under acceleration- time graph is equal to the change in velocity- in the given time....

A particle starts with an initial velocity of \(10.0 \mathrm{~ms}^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0 \mathrm{~ms}^{-2}\). The time taken by the particle to reach the velocity of $$60.0 \mathrm{~ms}^{...

A horse rider covers half the distance with \(5 \mathrm{~m} / \mathrm{s}\) speed. The remaining part of the distance was travelled with speed \(10 \mathrm{~m} / \mathrm{s}\) for half the time and with speed \(15 \mathrm{~m} / \mathrm{s}\) f...

Match Column-I with Column-II :

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A vehicle travels $4 \mathrm{~km}$ with speed of $3 \mathrm{~km} / \mathrm{h}$ and another $4 \mathrm{~km}$ with speed of $5 \mathrm{~km} / \mathrm{h}$, then its average speed is

A tennis ball is dropped on to the floor from a height of 9.8 m. It rebounds to a height 5.0 m. Ball comes in contact with the floor for 0.2s. The average acceleration during contact is ___________ ms\(^{-2}\).
(Given g = 10 ms\(^{-2}\))

A car travels a distance of '\(x\)' with speed \(v_1\) and then same distance '\(x\)' with speed \(v_2\) in the same direction. The average speed of the car is :

The distance travelled by a particle is related to time t as \(x=4\mathrm{t}^2\). The velocity of the particle at t=5s is :-

The velocity time graph of a body moving in a straight line is shown in the figure.

The ratio of displacement to distance travelled by the body in time 0 to 10s is :

An object moves with speed \(v_1,v_2\) and \(v_3\) along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3AB, then average speed of the object will be:

For a train engine moving with speed of \(20 \mathrm{~ms}^{-1}\), the driver must apply brakes at a distance of 500 \(\mathrm{m}\) before the station for the train to come to rest at the station. If the brakes were applied at half of this d...

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

Two trains 'A' and 'B' of length '\(l\)' and '\(4 l\)' are travelling into a tunnel of length '\(\mathrm{L}\)' in parallel tracks from opposite directions with velocities \(108 \mathrm{~km} / \mathrm{h}\) and $$72 \mathrm{~km} / \mathrm{h}$...

A passenger sitting in a train A moving at \(90 \mathrm{~km} / \mathrm{h}\) observes another train \(\mathrm{B}\) moving in the opposite direction for \(8 \mathrm{~s}\). If the velocity of the train B is \(54 \mathrm{~km} / \mathrm{h}\), th...

The distance travelled by an object in time \(t\) is given by \(s=(2.5) t^{2}\). The instantaneous speed of the object at \(\mathrm{t}=5 \mathrm{~s}\) will be:

A ball is thrown vertically upward with an initial velocity of \(150 \mathrm{~m} / \mathrm{s}\). The ratio of velocity after \(3 \mathrm{~s}\) and \(5 \mathrm{~s}\) is \(\frac{x+1}{x}\). The value of \(x\) is ___________.
\(\left\{\right.\)...

From the \(\mathrm{v}-t\) graph shown, the ratio of distance to displacement in \(25 \mathrm{~s}\) of motion is:

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 th...

A person travels \(x\) distance with velocity \(v_{1}\) and then \(x\) distance with velocity \(v_{2}\) in the same direction. The average velocity of the person is \(\mathrm{v}\), then the relation between \(v, v_{1}\) and \(v_{2}\) will b...