The position of a particle moving along x-axis is given by x = 3 $t^{2}$ - t³ where x is in m and t is in s. Consider the following statements :
(i) Displacement of the particle in first 4 s is 16 m.
(ii) Distance travelled by the particle upto 4 s is 24 m.
(iii) Displacement of the particle in first 4 s is 16 m.
(iv) Distance covered by the particle upto 4 s is 22 m.
Select the CORRECT alternative :

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statements (i) and (iii) are correct

statements (i) and (ii) are correct

statements (ii) and (iii) are correct

none of the above

answer is B.

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Detailed Solution

x = 3t²- $t^{3}$ $\Rightarrow$ v = 6t - 3t² = 3t(2-t)
At t=0,x = 0 and v = 0
At t = 2s,x = 4 m, v = 0 (reverses its direction)
A t = 4s, x = -16m

In first 4s, distance = 4 + 4 + 16 = 24 m
Displacement = -16 m

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