Motion in A Plane

The speed of the projectile at its maximum height is half of its initial speed. The angle of projection is

• 60^o

• 15^o

• 30^o

• 30^o

A particle moves in the x-y plane according to rule x = a sin ωt and y = a cos ωt. The particle follows

• an elliptical path

• a circular path 

• a parabolic path

• a parabolic path

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s₁ and that covered in the first 20 s is s₂, then

• s₂ = 2s₁

• s₂ = 3s₁

• s₂ = 4 s₁

• s₂ = 4 s₁

Two bodies of mass 1 kg have position vectors,  respectively.The centre of mass of this system has a position vector

If  is the force acting on a particle having position vector  be the the torque of this force about the origin, then

The distance travelled by a particle starting from rest and moving with an acceleration 4/3 ms^-2 in the third second is

• 6 m

• 4 m

• 10/3

• 10/3

A particle shows distance -time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

• B

• C

• D

• D

A particle moves in a straight line with a constant acceleration. It changes its velocity from 10 ms^-1 to 20 ms^-1 while passing through a distance 135 m in t second.  The value of t is 

• 10

• 1.8

• 12

• 12

A particle of mass is projected with the velocity v making an angle of 45^o with the horizontal. 
When the particle  lands on the level ground the magnitude of the change in its momentum will be

• 2 mv

• 
• 
• 

The position x of a particle with respect to time t along x- axis is given by x = 9t² -t³ where x is in meter and t in second. What will be the position of this particle when it achieves maximum speed along the +x direction? 

• 32 m

• 54 m

• 81 m 

• 81 m