Motion in a straight line practice · Easy

Statement I : Two objects moving with velocities $v_1$ and $v_2$ in the opposite directions, have their relative velocity along the direction of the one with a larger velocity.

Statement II : The relative velocity between two bodies moving with velocity $\mathbf{v}_1$ and $\mathbf{v}_2$ in same direction is given by $\mathbf{v}=\mathbf{v}_1-\mathbf{v}_2$

A room has dimensions $3\,m \times 4\,m \times 5\,m$. A fly starting at one comer ends up at the diametrically opposite conner. The magnitude of the displacement of the fly is

The distance travelled by a particle is directly proportional to $\sqrt{t}$, where $t$ is time elapsed. Which of the following is correct regarding the motion of the particle?

A train is moving slowly on a straight track with a constant speed of $2 \mathrm{~m} \mathrm{~s}^{-1}$. A passenger in that train starts walking at a steady speed of $2 \mathrm{~m} \mathrm{~s}^{-1}$ to the back of the train in the opposite direction of the motion of the train. So, to an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be

If a body is moving along a straight path then which of the following is true?

A very large number of balls are thrown vertically upwards in quick succession in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is 5m, the number of ball thrown per minute is (take $g = 10\;m{s^{ - 2}}$)

A hall has dimensions $10\,m \times 12\,m \times 14\,m$. A fly starting at one corner ends up at a diagonally opposite corner what is the magnitude of distance if it travels along three edges of hall

A particle covers equal distance around a circular path, in equal intervals of time. Which of the following quantities connected with the motion of the particle remains constant with time?

If an object is falling freely in vacuum, then body moves with

A body is thrown vertically upwards with a velocity u. Find the true statement from the following

A particle covers half of its total distance with speed ${v_1}$ and the rest half distance with speed ${v_2}$. Its average speed during the complete journey is

A police jeep is chasing a culprit going on a motor bike. The motor bike crosses a turning at a speed of 72 km/h. The jeep follows it a speed of 90 km/h crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike? (in km)

An object is projected upwards with a velocity of 100m/s. It will strike the ground after (approximately)

If distance covered by a particle is zero, what can you say about its displacement?

A body is thrown vertically upward from a point $A$ $125 \mathrm{~m}$ above the ground. It goes up to a maximum height of $250 \mathrm{~m}$ above the ground and passes through $A$ on its downward journey. The velocity of the body when it is at a height of $70 \mathrm{~m}$ above the ground is (Take, $g=10 \mathrm{~ms}^{-2}$ )

For a body travelling with uniform acceleration, its final velocity is $V = \sqrt {180 - 7x}$, where $x$ is the distance travelled by the body then the acceleration is

A body falls for 5 s from rest. If the acceleration due to gravity of earth ceases to act, the distance it develops in the next 3 s is

A body thrown vertically upward with an initial velocity of 1.4 m/s returns in 2s. The total displacement of the ball is

If Position of a particle is given by $x=\left(4 t^2-8 t\right)$, then which of the following is true?

Assertion (A): Speed of a particle may decrease, even if acceleration is increasing.

Reason (R): This will happen if acceleration is positive.

A particle moving with uniform acceleration has its final velocity $(v = \sqrt {150 + 8x} )\,\,m\mathrm{/}s$ where $x$ is the distance travelled by the body then the acceleration

A car travels equal distances in the same direction with velocities $60\mathrm{km}{\mathrm{h}^{ - 1}}\,,\,20\;\mathrm{km\;}{\mathrm{h}^{ - 1}}$ and $10\;\mathrm{km\;}{\mathrm{h}^{ - 1}}$ respectively. The average velocity of the car over the whole journey of motion is

The velocity of light in vaccum is $3 \times {10^8}\,m/s$. Calculate the time taken by it to travel a distance of $6 \times {10^{14}}\,m$

Velocity of a body on reaching the point from which it was projected upwards, is

The x and y coordinates of a particle at any time $t$ are given by $x = 8{t^2} + 5{t^3}$ and $y = 2t$. Where x and y are in metre and $t$ in seconds. The acceleration of particle at $t = 5$ sec is

A police jeep is chasing with velocity of $45 \mathrm{~km} / \mathrm{h}$ a thief in another jeep moving with velocity $153 \mathrm{~km} / \mathrm{h}$. Police fires a bullet with muzzle velocity of $180 \mathrm{~m} / \mathrm{~s}$. The velocity with which it will strike the car of the thief is

The velocity $\mathrm{v}$ of a particle is given by the equation $v=6 t^2-6 t^3$ where $v$ is in $\mathrm{m} / \mathrm{sec}$ and $\mathrm{t}$ is time in seconds then :

If a cyclist takes one minute to complete half revolution on a circular path 120 m radius. What is the average velocity?

The displacement of a body along $X$-axis depends on time as $\sqrt{x}=t+1$. Then, the velocity of body

The motion of a particle in straight line is an example of