Embibe Experts Solutions for Chapter: Kinematics, Exercise 1: JEE Main - 1 September 2021 Shift 2

The speed of a swimmer is $4 \mathrm{km} {\mathrm{h}}^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of river of width $1 \mathrm{km}$, he reaches a point $750 \mathrm{m}$ down the stream on the opposite bank. The speed of the river water is ______ $\mathrm{km} {\mathrm{h}}^{-1}$.

A body is moving with constant speed, in a circle of radius $10 \mathrm{m}$. The body completes one revolution in $4 \mathrm{s}$. At the end of $3rd$ second, the displacement of body (in $\mathrm{m}$) from its starting point is:

A stone of mass $1\mathrm{kg}$ is tied to end of a massless string of length $1 \mathrm{m}$. If the breaking tension of the string is $400 \mathrm{N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

Two bodies are projected from ground with same speeds $40 \mathrm{m} {\mathrm{s}}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60°$, with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ $\mathrm{m}$. (Given $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

An object moves with speed $v_1, v_2 \text{and} v_3$ along a line segment $AB, BC \text{and} CD$ respectively as shown in figure. Where $AB = BC \text{and} AD = 3 AB$, then average speed of the object will be :

A child stands on the edge of the cliff $10 \mathrm{m}$ above the ground and throws a stone horizontally with an initial speed of $5 \mathrm{m} {\mathrm{s}}^{–1}$ . Neglecting the air resistance, the speed with which the stone hits the ground will be _____ $\mathrm{m} {\mathrm{s}}^{–1}$ (given, $g = 10 \mathrm{m} {\mathrm{s}}^{–2 }$ ).

For a body projected at an angle with the horizontal from the ground, choose the correct statement

For a train engine moving with speed of $20 {\mathrm{ms}}^{–1}$, the driver must apply brakes at a distance of $500 \mathrm{m}$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{x} {\mathrm{ms}}^{-1}$. The value of $x$ is ______. (Assuming same retardation is produced by brakes)