Question

The position(x) of a particle varying with time(t) is
given by x = (t^2 - 6t) m. The distance covered by
particle in first 6 s will be
(1) 6 m
(2) 9 m
(3) 15 m
4) 18 m ​

Answer 1

answer : option (4) 18m

explanation : The position of a particle varying with time is given as x = (t² - 6t)

differentiating x with respect to time,

dx/dt = 2t - 6

now putting, dx/dt = 2t - 6 = 0

⇒t = 3

hence, particle becomes rest at t = 3s

so, distance covered by particle in first 6s = |x(t = 3) - x(t = 0)| + |x(t = 6) - x(t - 3)|

= |3² - 6(3) - 0² - 6(0)| + |6² - 6(6) - 3² + 6(3)|

= |9 - 18| + |-9 + 18|

= 9 + 9

= 18m

hence, option (4) is correct choice.

Answer 2

$\huge\bold\purple{Answer:-}$

4) 18 m