First slide

Position Path Length (Distance) And Displacement

Question

The displacement of a particle is given by x = (t - 2)² where x is in meters and t in seconds. The distance covered by the particle in first 4 seconds

Moderate

A

4 m
B

8 m
C

12 m
D

16 m

Solution

Velocity of the particle $v = \frac{dx}{dt} = 2 (t - 2)$ . Hence particle changes direction at t=2 as velocity changes from negative to positive at that instant.
Therefore total distance covered by the particle from t=0 to t=4 $= |x_{t = 2} - x_{t = 0}| + |x_{t = 4} - x_{t = 2}| = 4 + 4 = 8 m$

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