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#### The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10 s−1.  At, t=0 the displacement is 5 m.  What is the maximum acceleration ?  The initial phase IS Option: 1 500 m/s2   Option: 2  Option: 3 750 m/s2   Option: 4 m/s2

As learnt in   At   Maximum acceleration =   #### A particle is moving along the x- axis with its coordinate with time 't' given by . Another particle is moving along the y-axis with its coordinate as a function of time given by  At  s, the speed of the second particle measured in the frame of the first particle is given by . Then  (in m/s) is ____________. Option: 1 580 Option: 2 700 Option: 3 100 Option: 4 300

At time t= 1 s

So the value of v is 580

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• Faculty Support #### A ball is dropped from the top of a 100 m high tower on a planet. In the last s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity ( in ms-2) near the surface on that planet is _______. Option: 1 8 Option: 2 4 Option: 3 2 Option: 4 6

Let the total time taken by the particle is t

So distance covered by a particle in t sec=

Similarly, distance covered by particle in sec=

So  distance covered by particle in last (1/2) sec of its journey=

So

and

from equations (1) and (2)

we get

putting t=5 we get g = 8 m/s2

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• Faculty Support #### A particle moves such that its position vector where is a constant and t is time. Then which of the following statements is true for the velocity  and acceleration  of the particle :  Option: 1 and both are parallel to Option: 2 is perpendicular to and is directed away from the origin Option: 3 and both are perpendicular to Option: 4 is perpendicular to and is directed towards the origin

implies a is anti parallel to r

Implies v is perpendicular to r

hence the correct option is (4).

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• Faculty Support #### The sum of two forces   and  is such that  The angle  (in degrees) that the resultant of  and  will make with  is , Option: 1 90 Option: 2 120 Option: 3 45 Option: 4 30

As

Now Vector P is doubled but vector Q is the same so the angle between  will be also

And If resultant of  is

Then from the figure angle between  is

and

#### A car accelerates from rest at a constant rate for sometime after which it decelerates at a constant rate to come to rest. If the total time elapsed is t seconds, the total distance travelled is :Option: 1 Option: 2 Option: 3 Option: 4 Let the car accelerate for time traveling distance and acquire maximum velocity v.
Then, [from the equation, ]
and   [from the equation, v=u+a t ]

After this car decelerates for time  to come to rest
Hence,        [from the equation, ]
and          [from the equation, u=v-a t ]

Also, total distance traveled,

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• Faculty Support #### A swimmer wants to cross a river from point to point . Line makes an angle of with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle with the line should be _______ swimmer reaches point    #### The magnitude of vectors in the given figure are equal. the direction of with x-axis will be: Option: 1 Option: 2 Option: 3 Option: 4   The correct option is (2)  