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The position of a particle travelling along x axis is given by $x_{1}=t_{3}−9t_{2}+6t$ where $x_{t}$ is in $cm$ and $t$ is in second. Then

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1

The position of a particle travelling along x axis is given by $x_{1}=t_{3}−9t_{2}+6t$ where $x_{t}$ is in $cm$ and $t$ is in second. Then

This question has multiple correct options2

From point $A$ located on a highway (shown in figure above) one has to get by car as soon as possible to point $B$ located in the field at a distance $l$ from the highway. It is known that the car moves in the field $η$ times slower than on the highway. At a distance $CD=η_{2}−1 xl $ from point $D$ one must turn off the highway. Find $x$.

3

A driver takes $0.20s$ to apply the brakes after he sees a need for it. This is called the reaction time of the driver. If he is driving a car at a speed of $54km/h$ and the brakes causes a deceleration of $6.0m/s_{2}$, find the distance traveled by the car after he sees the need to put the brakes on.

4

Two particles A and B move with velocities $v_{1}andv_{2}$ respectively along the x and y axis. The initial separation between them is 'd' as shown in the figure. Find the least distance between them during their motion

5

Two particles instantaneously at $A$ and $B$ are $5m$, apart and they are moving with uniform velocities, the former towards $B$ at $4m/s$ and the latter perpendicular to $AB$ at $3m/s$. They are nearest at the instant (in seconds)

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A particle is thrown vertically upward with a speed of 100 m/s . What is distance of particle travelled in 15 sec ?

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A train stops at two stations P and Q which are 2 km apart, It accelerates uniformly from $Pat1ms_{2}$ for 15 seconds and maintains a constant speed for a time before decelerating uniformly to rest at Q. If the deceleration is $0.5ms_{2}$, find the time for which the train is travelling at a constant speed.

8

Starting from rest a particle moves in a straight line with acceleration

$a=(25−t_{2})_{1/2}m/s_{2}for0≤t≤5s$

$a=83π m/s_{2}fort≥5s$

The velocity of particle at t = 7s is:

$a=(25−t_{2})_{1/2}m/s_{2}for0≤t≤5s$

$a=83π m/s_{2}fort≥5s$

The velocity of particle at t = 7s is:

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A street car moves rectilinearly from station $A$ (here car stops) to next station $B$ (here also car stops) with an acceleration varying according to the law $f=a−bx$, where $a$ and $b$ are positive constants and $x$ is the distance from station $A$. If the maximum distance between the two stations is $x=bNa $ then find $N$.

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A hunter is at $(4,−1,5)$ units. He observes two preys at $P_{1}(−1,2,0)$ units and $P_{2}(1,1,4)$ respectively. At zero instant he starts moving in the plane of their positions with uniform speed of $5unitss_{−1}$ in a direction perpendicular to line $P_{1}P_{2}$ till he sees $P_{1}$ and $P_{2}$ collinear at time $T$. Time $T$ is