Displacement Vector

Understanding Rest And Motion|Frame Of Reference|Introduction To Mechanics|Kinematics|Motion In A Straight Line|Practice Exercise|Position Vector And Displacement Vector|Distance And Displacement|Average Speed And Average Velocity|Instantaneous Velocity And Instantaneous Speed|Average And Instantaneous Acceleration|Practice Exercise|Summary

There are two vectors Force vec(A) = (hat(i) + 3 hat(j) - hat(k)) N and Position vec(B) = (hat(i) + 3 hat(j) - hat(k))m that can be used by two students Alia and Varun. Following are the steps following by each of them. Alia : Step 1 : Calculate unit vector of vec(A) by dividing it by its magnitude and get hat(A) = (hat(i) + 3 hat(j) - hat(k))/(sqrt11) Alia : Step 2 : Get a displacement vector of magnitude 10m using hat(A) Displacement vector = (10(hat(i) +3 hat(j) - hat(k))/(sqrt11)) m Varun : Step 1 : Calculate unit vector of vec(B) by dividing vec(B) by its magnitude and get, hat(B) = ((hat(i) + 3 hat(j) - hat(k))/(sqrt11)) Varun : Step 2 : Get a force vector of magnitude 10 N by using vec(B) Force vector = (10(hat(i) + 3 hat(j) - hat(k)) N)/(sqrt11) Siddharth, a third student, comes and says when we divide or multiply a vector by a scalar, then the physical quantity represented by the vector from a displacement vector from a force vector or a force vector from a displacement vector as calculated by Alia and Varun repectivley. Who is/are correct ?

A particle travels with constant speed on a circle of radius 3 metres and completes one revolution in 20 seconds. Starting from origin O, find the magnitude and direction of displacement vector 5 seconds later -

Assertion: A balloon ascends from the surface of earth with constant speed. When it was at a height 50 m above the ground, a packet is dropped from it. To an observer on the balloon, the displacement of the packet, from the moment it is dropped to the moment it reaches the surface of earth, is 50 m Reason: Displacement (vector) depends upon the reference frame used to measure it.

From a tower of height 40 m , two bodies are simultaneously projected horizontally in opposite direction, with velocities 2 m s^-1 and 8 ms^-1 . respectively. The time taken for the displacement vectors of two bodies to be come perpendicular to each other is.

Read each statement below carefully and state with reasons, with it is true or false : (a) The magnitude of vector is always a scalar. ltBrgt (b) Each component of a vector is alwarys a scalar. (c ) The total path length is always equal to the magnitude of the displacement vector of a particle. (d) The average speed of a particle (defined as total path length diveked by the time taken to cover the path ) is eigther greater or equal to the magnitude of average velocity of the particle over the same interval of time. ltbRgt (e ) three vectors not lying in a planc ecan never add up to give a null vector.

A particle travels with constant speed along a circle of radius 3 m and completes one revolution in 20 s . Starting with the lowest point as origin, find (a) the magnitude and direction of the displacement vectors 5 s, 7.5s and 10 s later , (b) the magnitude and direction of the displacement in the 5 s interval from the fifth to the lenth second, (c) average velocity in this interval, (d) the instantaneous velocity at the begining and at the end of the interval.