Answer
12 m
Work Step by Step
To find the displacement between t = 0 and t = 4 we need to find the difference between the position at t=0 and the position at t =4.
The position is given by the equation $ x = 3t - 4t^2 + t^3 $ where x is in meters and t is in seconds
To find the position at t = 0 s we need to find x(0), or in other words, plug in 0 for t in the equation and teo find the position at t = 4s, we do the same for 4. This gives us :
For t = 0:
$ x = 3(0) - 4(0)^2 + (0)^3 = 0 -4*(0) + 0 = 0 - 0 + 0 = 0 $
Therefore at t =0, x = 0
For t = 4:
$ x = 3(4) - 4(4)^2 + (4)^3 = 12 - 64 + 64 = 12 $
Therefore at t = 4, x = 12
To find the displacement we take x(4) - x(0), which is 12m - 0m = 12m
