Motion in a straight line practice · Medium

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 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 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.

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 $\mathrm{g} = 10\mathrm{m}{\mathrm{s}^{ - 2}}$)

Two trains, each of length $100 \mathrm{~m}$, are running on parallel tracks. One overtakes the other in $20 \mathrm{sec}$. and one crosses the other in opposite direction 10 sec. Calculate the velocities of each train.

A point moves in a straight line, so that its displacement $x$ at time $t$ is given by $x^2=t^2+1$. Its acceleration is

The numerical ratio of displacement to distance for a moving object is

Two bodies are held separated by $9.8 \mathrm{~m}$ vertically ane above the other. They are released simultaneously to fall freely under gravity. After $2 \mathrm{~s}$, the relative distance between them is

The numerical ratio of displacement to distance is

Velocity – time graph of a body thrown vertically up is

If $V=\alpha \sqrt{x}, \mathbf{V}$ is velocity, $\mathbf{x}$ is position, $\mathbf{a}$ is +ve constant then $\mathbf{a}=$ ?

A particle moves in a straight line as $s = \alpha \left( {t - 4} \right) + \beta {\left( {t - 4} \right)^2}$. Find the initial velocity and acceleration.

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

Which of the following statements, is incorrect regarding motion of particle along straight line?

Statement-I: In successive time intervals if the average velocities of a particle are equal then the particle must be moving with constant velocity.
Statement-II: When a particle moves with uniform velocity, its displacement always increases with time.

What determines the nature of the path followed by the particle

A man leaves his house for a cycle ride. He comes back to his house after half-an-hour after covering a distance of one $\mathrm{km}$. What is his average velocity for the ride?