Distance vs. Displacement

Classical Mechanics Level 1

A particle constrained to one dimension starts at x = 0 x=0 , moves to the right to the point x = 4 x=4 , and then moves to the left to x = − 2 x=-2 . If a a is the displacement of the particle after this process and b b is the distance traveled, find a + b a+b .

-2 4 8 10

Matt DeCross by Matt DeCross , 27, USA

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3 solutions

We clearly see that the total distance from x = − 2 x=-2 to x = 4 x=4 is b = 6 b=6 and the distance covered from x = − 2 x=-2 to x = 0 x=0 is a = 2 a=2 . Thus a + b = 2 + 6 = 8 a+b=2+6=8 .

7 Helpful 0 Interesting 0 Brilliant 0 Confused

is the displacement negative? .should we not consider the negative sign?

Ananya Phadnis - 1 year, 2 months ago
Zachariah Watson
Aug 21, 2018

Initial: x = 0

  1. x = 4 ; Displacement from Initial: 4 ; Step distance traveled: 4 ; Total distance traveled: 4

  2. x = -2 ; Displacement from Initial: -2 ; Step distance traveled: 6 ; Total distance traveled: 10

Final: x = -2 ; Displacement from initial = -2 ; Total distance traveled: 10

a = displacement; -2

b = total distance traveled; 10

a + b = ?

-2 + 10 = ?

Answer: 8

0 Helpful 4 Interesting 2 Brilliant 3 Confused

I thought that since displacement is a vector quantity and thus requires a direction, we include the negative sign of -2, therefore, a+b = (-2)+6 = 4

Simon Paulino - 1 year, 8 months ago
Rishabh Tiwari
May 10, 2016

We can clearly see that total distance travelled= 4+6=10 & displacement = -2i^ m Hence a+b = 10-2=8. Ans.

3 Helpful 0 Interesting 0 Brilliant 2 Confused

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