Test: Position, Path Length and Displacement - ACT MCQ

The path length depends on the final and initial point. It also depends on the path taken. But it does not depend on the coordinate system. The coordinate system merely defines thee path and does not affect its total length.

In Spherical system, distance from the center, the angle with the X axis, and the angle with the Z axis are used to define the position of a point. These are respectively represented by R, θ and ф.

The distance depends on the final and initial points as these points define the path. Distance also depends on the path chosen, the distance between same initial and final point with different paths can be different. It does not depend on speed as whatever the speed may be, if the initial and final points and path remains same, the distance remains same.

The displacement is the distance between the final and the initial location. Here the final location is C and the initial is A. We can solve this by using distance between two points method. AC = Square root ((8² – 0²) + (6² – 0²)) = Square root (100) = 10 units.

In one turn the person covers 5 – (-2) units of distance, i.e. 7. Therefore in 5 turns, he will cover 5 x 7 = 35 units of distance.

The vertical distance between A and B is of 2 units and the horizontal distance is 1 unit. Hence, to calculate the displacement, we can make a right-angled triangle as shown and can find the distance (AB) by Pythagoras theorem. Distance (AB) = Square root (2² + 1²) = Square root (5).

The displacement covered in the first five seconds can be obtained by putting t = 5 in the equation. Therefore, x = 5⁵ + 2(5) = 25 + 10 = 35. Hence the answer is 35 units.

Displacement is the shortest distance between two points. Hence displacement <= distance or vice versa. If the path followed is the path of shortest distance or displacement, then displacement = distance.

Total path length = Sum of path lengths of intermediate paths. Therefore, Path length AD = Sum of Path lengths of AB, BC, CD = 5 + 5 + 5 = 15 units.

Displacement between two points is the shortest path between them. It is always less than or equal to the distance between them. Displacement can never be greater than distance.