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

Question

The displacement of a particle is given by x = (t - 2)2 where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is m (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Given: x = (t - 2)2 At t = 0 , x = x0 = (0 - 2)2 = 4 m t = 1 s , x = x1 = (1 - 2)2 = 1 m t = 2 s , x = x2 = (2 - 2)2 = 0 m t = 3 s , x = x3 = (3 -2)2= 1 m t = 4 s , x = x4 = (4 - 2)2 = 4 m The distance covered by the particle in 1st second is D1 = x0 - x1 = 3 m The distance covered by the particle in II nd second is D2 = x1 - x2 = 1 m Similarly, D3= 1 m , D4 = 3 m The distance covered by the particle in first 4 seconds is D = D1 + D2 + D3 + D4 = 3 m + 1 m + 1 m + 3 m = 8 m

Q. The displacement of a particle is given by x=(t−2)2 where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is______ m

Q. The displacement of a particle is given by $x = (t - 2)^{2}$ where $x$ is in metres and $t$ in seconds. The distance covered by the particle in first $4$ seconds is______ m