Motion in a Straight Line

The relation between the displacement ' $x$ ' (in metre) and the time ' $t$ ' (in second) of a particle is $t=2 x^2+3 x$. If the displacement of the particle is 25 cm from the origin $(x=0)$, then the acceleration of the particle is

For a particle moving along a straight line path, the displacements in third and fifth seconds of its motion are 10 m and 18 m respectively. The speed of the particle at time $t=4 \mathrm{~s}$ is

A particle initially at rest is moving along a straight line with an acceleration of $2 \mathrm{~ms}^{-2}$. At a time of 3 s after the beginning of motion, the direction of acceleration is reversed. The time from the beginning of the motion...

A person wearing a parachute jumps off a plane from a height of 2 km from the ground and falls freely for 20 m before his parachute opens. After his parachute opens if he continues to move uniformly with the velocity attained due to his fre...

The initial and final velocities of a body projected vertically from the ground are $20 \mathrm{~ms}^{-1}$ and $18 \mathrm{~ms}^{-1}$ respectively. The maximum height reached by the body is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2...

The driver of a bus moving with a velocity of $72 \mathrm{~km} / \mathrm{h}$ observes a boy walking across the road at a distance of 50 m in front of the bus and decelerates the bus at $5 \mathrm{~ms}^{-2}$ by applying brakes and is just ab...

A body projected vertically up with an initial speed of $10 \mathrm{~ms}^{-1}$ reaches the point of projection after sometime with a speed of $8 \mathrm{~ms}^{-1}$. The maximum height reached by the body is
(Acceleration due to gravity $=10...

The ratio of times taken by a freely falling body to travel first 5 m , second 5 m , third 5 m distances is

A body is falling freely from the top of a tower of height 125 m . The distance covered by the body during the last second of its motion is $x \%$ of the height of the tower. Then, $x$ is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$...

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. The time taken by the stone to cross the window during its downward journey is (acceleration due to gravity $=10 \mathrm{...

The position $x$ (in metre) of a particle moving along a straight line is given by $x=t^{3}-12 t+3$, where $t$ is time (in second). The acceleration of the particle when its velocity becomes $15 \mathrm{~ms}^{-1}$ is

A body moving with uniform acceleration, travels a distance of 25 m in the fourth second and 37 m in the sixth second. The distance covered by body in the next two seconds is

A body is thrown vertically upwards with a velocity of $35 \mathrm{~ms}^{-1}$ from the ground. The ratio of the speeds of the body at times 3 s and 4 s of its motion is (acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

The acceleration of a vertically projected body at its highest reaching position is

The displacement-time graphs of two moving particles make angles of $30^{\circ}$ and $45^{\circ}$ with the time axis. The ratio of their velocities is

A body starts rest with uniform acceleration. If its velocity after $n^{\text {th }}$ second (last second) is $v$ then its displacement in the last two seconds is

A bird flies with a velocity $(t-2) \mathrm{ms}^{-1}$ along a straight line, where $t$ is the time in seconds. The distance covered by it in a time of 4 seconds is

The relation between time $t$ and distance $x$ of a particle is $t=a x^2+b x$, where $a$ and $b$ are constants. If $v$ is the velocity of the particle, then its acceleration is

The ratio of the displacements of a freely falling body during first, second and third seconds of its motion is

Two towns $X$ and $Y$ are connected by a regular bus service. A bus leaves in either direction at every $t=T$ minutes. A man moving with same speed in the direction $X$ to $Y$ find that a bus goes past him every $t=t_1$ minutes in the direc...

A ball projected up passes the same height $H$ at 2 s and 10 s . The value of $H$ is (use, $g=9.8 \mathrm{~m} / \mathrm{s}^2$ )

A car starts at time $t=0$ from an initial speed of $10 \mathrm{~m} / \mathrm{s}$ and accelerates uniformly with $2 \mathrm{~m} / \mathrm{s}^2$ on a straight road for time $0 \leq t \leq 10 \mathrm{~s}$. Let $s_1$ and $s_2$ be the distance ...

An aircraft is flying at a height of $h$ above the ground and at a speed of $v$. The maximum angle subtended at a ground observation point by the aircraft after time $t$ is

A particle moves along a straight line, such that its displacement $x$ varies with time $t$ as $x=\alpha t^3+\beta t^2+\gamma$, where $\alpha, \beta$ and $\gamma$ are constants, $v_1$ is the average velocity of the particle during its journ...

A rocket moves straight upward with zero initial velocity and with an acceleration $20 \mathrm{~m} / \mathrm{s}^2$. It runs out of fuel and stops accelerating at the end of 5th second. It reaches a maximum height and falls back to the earth...

A bullet fired into a target losses one-third of its velocity after travelling a distance $x$ metre into the target. If the bullet comes to rest by travelling a further distance $x^{\prime}$, then the ratio $\frac{x^{\prime}}{x}$ is

A body starts from the rest and acquires a velocity of $10 \mathrm{~m} / \mathrm{s}$ in 2s. What is the acceleration of the body and the distance travelled?

A particle starts from rest. Its acceleration (a) versus time $(t)$ graph is as shown in the figure. The maximum speed of the particle will be

A river has a steady speed of $v$. A man swims upstream at a distance of $d$ and swims back to the starting point in total time $t$. The man can swim at a speed of $2 v$ in still water. If the time taken by the man in still water is $t_0$ t...

Assertion (A) The zero velocity of a particle at any instant always implies zero acceleration at that instant.
Reason (R) A body is momentarily at rest when it reverses its direction of motion. The correct option among the following is

A body moves in a straight line with speed $v_1$ and $v_2$ for distance which are in ratio $1: 2$. Find the average speed.

A motor-bike starts from rest, attains a velocity of 10 $\mathrm{m} / \mathrm{s}$ with an acceleration of $0.5 \mathrm{~m} / \mathrm{s}^2$, travels 10 km with this uniform velocity and then comes to halt with a uniform deceleration of $0.2 ...

A ball is thrown straight upward from ground with a speed of $20 \mathrm{~m} / \mathrm{s}$. The ball was caught on its way down at a point 5 m above the ground. The time taken by the ball during entire trip is (assume, $g=10 \mathrm{~m} / \...

A particle moving along $X$-axis has acceleration $f$ at time $t$ given by $f=f_0\left(1-\frac{t}{T}\right)$, where $f_0$ and $T$ are constants. The particle at $t=0$ has zero velocity. In the time interval between $t=0$ and the instant whe...

A ball is thrown vertically upwards with an initial velcoity $u$ reaches maximum height in 5 s . The ratio of distance travelled by the ball in the 2nd and 7th second is (assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ )

Consider that a truck is moving initially with $54 \mathrm{~km} / \mathrm{h}$. It has stopped by the driver after looking at an obstacle with a deceleration of $10 \mathrm{~m} / \mathrm{s}^2$. The distance travelled by truck before coming t...

A car travelling at $15 \mathrm{~m} / \mathrm{s}$ overtake another car travelling at $10 \mathrm{~m} / \mathrm{s}$. Assuming, each car is 4 m long. What is the time taken during the overtake?

A particle is moving along the $Y$-axis. The position of the particle from the origin as a function of time $(t)$ is given as $y(t)=10 t e^{-2 t}$. How far is the particle from the origin when it stops momentarily? ( $y$ is given in units o...