1

**JEE Mains**

The distance x covered by a particle in one dimensional motion varies with time t as $x_{2}=at_{2}+2bt+c$. If the acceleration of the particle depends on x as $x_{−n}$, where n is an integer, the value of n is:

A particle moves such that its position vector $r(t)=cosωti^+sinωtj^ $ where $ω$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $v(t)$ and acceleration $a(t)$ of the particle:

A particle is moving along the x-axis with its coordinate with time '$t$' given by $x(t)=10+8t−3t_{2}$. Another particle is moving along the y-axis with its coordinate as a function of time given by $y(t)=5−8t_{3}$. At $t=1s$, the speed of the second particle as measured in the frame of the first particle is given as $v $. Then $v$ (in m/s) is ________.

A particle is moving with speed $v=bx $ along positive x-axis. Calculate the speed of the particle at time $t=τ$ (assume that the particle is at origin at $t=0$)

The position of a particle as a function of time t, is given by $x(t)=at+bt_{2}−ct_{3}$ where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be?

All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up.

A car is standing $200m$ behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2m/s_{2}$ and the car has acceleration $4m/s_{2}$. The car will catch up with the bus after a time of :

Two stones are thrown up simultaneously from the edge of a cliff $240m$ high with initial speed $10m/s$ and $40m/s$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ?

(Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10m/s_{2}$)

(The figures are schematic and not drawn to scale.)

(Assume stones do not rebound after hitting the ground and neglect air resistance, take $g=10m/s_{2}$)

(The figures are schematic and not drawn to scale.)

A person climbs up a stopped escalator in $60s$. If standing on the same escalator but escalator running with constant velocity, he takes 40 s. How much time is taken by the person to walk up in the moving escalator?