Motion in a Straight Line · Question 13

A particle moves along the x-axis and has its displacement x varying with time t according to the equation: x = c0 (t2 - 2 ) + c(t - 2)2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

1. the acceleration of the particle is 2(c + c0)
2. the acceleration of the particle is 2c0
3. the acceleration of the particle is 2c
4. the initial velocity of the particle is 4c

Answer

(1) the acceleration of the particle is 2(c + c0)

Solution

x = c0(t2 - 2) + c(t - 2)2

v = dxdt = 2c0t + 2c(t - 2)

a = dvdt = 2c0 + 2c = 2(c + c0)

Initial velocity (t = 0): v = -4c, not 4c.

∴ Only the first statement is correct.

Answer: (1)