Motion in a straight line practice · Mixed difficulty

If $v=(2 t+1) \mathrm{m} / \mathrm{sec}$ then average velocity from ${t}=0$ to $t=2\, \mathrm{sec}$ is

The correct statement from the following is

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

If initial velocity of a body is $\vec u = 2\hat i - 2\hat j + 3\hat k$ and is changed to $\vec v = 2\hat i - 4\hat j + 5\hat k$ in a time of 10sec. Its accelerated vector is

A point moves with a uniform acceleration and $v_1, v_2, v_3$ denote the average velocities in three successive intervals of time $t_1, t_2, t_3$. Which of the following relations is correct?

A bullet travelling with a velocity of $16 \mathrm{~m} / \mathrm{s}$ penetrates a tree trunk and comes to rest in $0.4 \mathrm{~m}$. Find the time taken during the retardation.

Assertion: A body dropped from a given height and another body projected horizontally from the same height strike the ground simultaneously.
Reason: Horizontal velocity has no effect in the vertical direction.

A particle moves with uniform velocity. Which of the following statements about the motion of the particle is true?

A ball is dropped from a building of height $45m$. Simultaneously another ball is thrown up with a speed $40\,m/s$. The rate of change of relative speed of the ball is

A particle moves in a straight line with a constant acceleration. It changes its velocity from $10\;m{s^{ - 1}}\,to\,20\;m{s^{ - 1}}$ while passing through a distance 135 m in t second. The value of t is

Which of the following statements is incorrect?

Speed of two identical cars are $u$ and $4 u$ at a specific instant. The ratio of the respective distance in which the two cars are stopped from that instant is

A body is thrown vertically upwards with a velocity $u$. Select the incorrect statements from the following.

I Both velocity and acceleration are zero at its highest point

II. Velocity is maximum and acceleration is zero at the highest point.

III. Velocity is maximum and acceleration is $g$ downwards at its highest point.

A car travelling at 108 km/hr its speed reduced to 36 km/hr while travelling a distance of 200 m. Its retardation and the time taken are

Assertion: The actual distance covered by an object in a given time interval can be equal to or greater than the magnitude of the displacement.

Reason: The distance covered is a scalar quantity, while the displacement is a vector quantity.

Assertion: The relative velocity between any two bodies moving in opposite direction is equal to sum of the
velocities of two bodies.

Reason: Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

A particle starts moving from rest under uniform acceleration. It travels a distance $x$ in the first $2 secons$ and a distance $y$ in the next $2 sec$. If $y = nx$ then $n$ is

A person walking at $4 {~m} / {s}$ finds rain drops falling slant wise in to his face with a speed of $4 {~m} / {s}$ at an angle of $30^{\circ}$ with the vertical. The actual speed of the rain drops is

A train of $150 \mathrm{~m}$ length is going toward north direction at a speed of $10 \mathrm{~m} \mathrm{~s}^{-1}$. A parrot flies at a speed of $5 \mathrm{~m} \mathrm{~s}^{-1}$ toward south direction parallel to the railway track. The time taken by the parrot to cross the train is equal to

A body is moving in a circular path with acceleration a. If its velocity gets doubled, find the ratio of acceleration after and before the change

A body is thrown vertically upwards in air, when air resistance is taken into account, the time of ascent is $t_1$ and time of descent is $t_2$, then which of the following is true?

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

A motor cyclist is riding North in still air at 36 $\mathrm{km} / \mathrm{h}$, the wind starts blowing westward with a velocity $18 \mathrm{~km} / \mathrm{h}$. The direction of apparent velocity is

A lift in which a man is standing, is moving upward with a speed of 10$\mathrm{m}{\mathrm{s}^{ - 1}}.$. The man drops a coin from a height of 4.9m and if g=9.8 $\mathrm{m}{\mathrm{s}^{ - 2}}$, then the coin reaches the floor of the lift after a time

The position vector of a moving particle at t sec is given by $\overrightarrow V = 3\hat i + 4{t^2}\hat j - {t^3}\hat k.$ Its displacement during an interval from 1s to 3s is.

A particle is moving on a straight line path with constant acceleration directed along the direction of instantaneous velocity. Which of the following statements are false about the motion of particle?

Statement-I: SHM is not an example of uniformly accelerated motion.

Statement-II: Non uniform velocity cannot give uniform acceleration

Assertion: If the displacement of the body is zero, the distance covered by it may not be zero.
Reason: Displacement depends only on endpoints; distance (path length) depends on the actual path.

A body falls from a height h=200m (at New Delhi). The ratio of distance travelled in each 2 sec during t=0 to t=6 second of the journey is

A ball dropped from the 9th story of a multi-storeyed building reaches the ground in 3s. In the first second of its free fall, it passes through n stories, where n is equal to (Take $\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$)