Question

A particle moves along a line according to the law s(t) = 2t³ – 9t² + 12t – 4, where t ≥ 0. Find the total distance travelled by the particle in the first 4 seconds

Answer 1

The distance travelled in the first 4 seconds is

|s(0) – s(1)| + |s(1) – s(2)| + |s(2) – s(3)| + |s(3) – s(4)|

Here, s(t) = 2t³ – 9t² + 12t – 4

s(0) = – 4

s(1) = 1

s(2) = 0

s(3) = 5

s(4) = 28

∴ Distance travelled in the first 4 seconds

= |-4 – 1| + |1 – 0| + |0 – 5| + |5 – 28|

= 5 + 1 + 5 + 23

= 34 m