A particle moves along the x-axis and its displacement varies with time as x = c₀(t²-2) + c(t-2)², where c₀ and c are constants of appropriate dimensions. Which statement is correct?
Options

Question

A particle moves along the x-axis and its displacement varies with time as x = c₀(t²-2) + c(t-2)², where c₀ and c are constants of appropriate dimensions. Which statement is correct?

G1 Physics · Accepted Answer

Given, x = c₀(t²-2) + c(t-2)². Differentiate with respect to time: v = dx/dt = 2c₀t + 2c(t-2). At t=0, v(0) = -4c, so option A is not correct as written. Differentiate once more: a = dv/dt = 2c₀ + 2c = 2(c+c₀). Therefore the acceleration is constant and equal to 2(c+c₀). Correct option: B.