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Find change in kinetic energy if a block...

Find change in kinetic energy if a block is displaced from (1,2) to (2,3) on applying a force of ` vec(F) = 4 x^2 hati + 3 y^2 hatj`

A

50.55J

B

60.55J

C

58.08J

D

68.08J

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A particle of mass 0.5 kg is displaced from position vec r_(1)(2,3,1) to vec r_(2)(4,3,2) by applying a force of magnitude 30 N which is acting along (hati + hatj + hatk) . The work done by the force is

(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk) and the plane vec(r).(hati - hatj + hatk) = 5. (ii) Find the distance of the point with position vector - hati - 5 hatj - 10 hatk from the point of intersection of the line vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - hatj + hatk)= 5. (iii) Find the distance of the point (2,12, 5) from the point of intersection of the line . vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk ) and the plane vec(r). (hati - 2 hatj + hatk ) = 0.

Find the angles between the following pairs of vectors: (i) vec(A) = hati + hatj +hatk and vec(B) =- 2hati - hatj - 2 hatk . (ii) vec(A) =- 2hati +2hatj - hatk and vec(B) = 3hati + 6 hatj +2 hatk (iii) vec(A) = 4 hati +6 hatj - 3 hatk and vec(B) =- 2hati - 5hatj +7 hatk

A varable force, given by the 2- dimensional vector overlineF=(3xx^(2)hati+4 hatj), acts on a particle. The force is in newton and x is in metre. What is the change in the kinetic energy of the particle as it moves from the point with coordinates (2,3) to (3,0) (The coornates are in metres)

An object has a displacement from position vector vecr_(1) = (2 hat i+3hatj)m to vecr_(2) = (4hat i + 6 hat j)m under a force vec F = (3x^(2) hati + 2y hatj)N , then work done by the force is

A block is displaced from (1m, 4m, 6m) to (2hati+3hatj-4hatk) m under a constant force F=(6hati-2hatj + hatk) N . Find the work done by this force.

Find the Cartesian equation of the following planes : a. vec(r). (hati + hatj - hatk ) = 2 b. vec(r). (2 hati + 3 hatj - 4 hatk ) = 1 (c ) vec(r). [ (s - 2t) hati + (3 - t ) hatj + (2 s + t ) hatk] = 15

A force vec(F) = 4 hati + hatj + 3hatk newton acts on a particle and displaces it through displacement vec(S) = 11 hati + 11 hatj +15 hatj metre. Calculate the work done by the force.

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