Question

the position of a particle is given by x=(3-t)^2 where x is in metre and t in second.the distance covered by particle in first 6 seconds is​

Answer 1

The position of particle is given by, x = (3 - t)² , where x is in metre and y in second.

here you can see that, position of particle at t = 3 is zero.

so, we have to find distance by two parts. first 0 ≤ t ≤ 3 and then 3 ≤ t ≤ 6

so, total distance covered by particle in 6 second = x(0 ≤ t ≤ 3) + x(3≤ t ≤ 6)

= |(3 - 3)² - (3 - 0)²| + |(3 - 6)² - (3 - 3)²|

= |0 -9 | + |9 - 0|

= 9 + 9

= 18

hence, distance covered in first 6 second is 18m