Motion In One Dimension

Assertion : The relative velocity between any two bodies may be equal to sum of the velocities of two bodies. Reason : Sometimes, relative velocity between two bodies may be equal to difference in velocities of the two.

A body released from a great height falls freely towards the earth. Another body is released from the same height exactly a second later. Then the separation between two bodies, $2 \mathrm{~s}$ after the release of the…

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 particle is thrown vertically up with an initial velocity $9 \mathrm{~m} / \mathrm{s}$ from the surface of Earth (take $g=10 \mathrm{~m} / \mathrm{s}^2$). The time (in s) taken by the particle to reach a height of $4…

Assertion : For a given time interval, average velocity is single valued while average speed can have many values. Reason : Velocity is a vector quantity and speed is a scalar quantity.

A body starts from rest and travels a distance $S$ with uniform acceleration, then moves uniformly a distance $2 S$ and finally comes to rest after moving further $5 S$ under uniform retardation. The ratio of the…

Assertion : If $a=-2 t$ for a particle moving in a straight linestartingwithan initialvelocity $4 \mathrm{~m} / \mathrm{s}$ from the origin, then distance travelled by it in $2 \mathrm{~s}$ is same as displacement.…

A body moves from rest with a constant acceleration. Which one of the following graphs represents the variation of its kinetic energy $K$ with the distance travelled $(x)$ ?

A ball is dropped from the top of a building $100 \mathrm{~m}$ high. At the same instant another ball is thrown upwards with a velocity of $40 \mathrm{~m} / \mathrm{s}$ from the bottom of the building. The two balls…

A man is at a distance of $6 \mathrm{~m}$ from a bus. The bus begins to move with a constant acceleration of $3 \mathrm{~m} \mathrm{~s}^{-2}$. In order to catch the bus, the minimum speed with which the man should run…

Assertion : The speedometer of an automobile measures the average speed of the automobile. Reason : Average velocity is equal to total distance divided by total time taken.

The displacement of a body is given to be proportional to the cube of time elapsed. The magnitude of the acceleration of the body is proportional to