Answer
(a) Yes, the particle has a turning point at t = 1 s.
(b) At t = 2 s:
x = 10 m
At t = 3 s:
x = 16 m
At t = 4 s:
x = 26 m
Work Step by Step
(a) Yes, the particle has a turning point at t = 1 s.
Note that at t = 1 s, the velocity is zero as it changes from a negative velocity to a positive velocity.
(b) The area between the velocity versus time graph and the x-axis is equal to the displacement.
From t = 0 to t = 2 s:
$\Delta x=0$
At t = 2 s:
$x=x_0+\Delta x$
$x=10 ~m+0$
$x=10 ~m$
From t = 2 to t = 3 s:
$\Delta x=6 ~m$
At t = 3 s:
$x=10 ~m+6 ~m$
$x=16 ~m$
From t = 3 to t = 4 s:
$\Delta x=10 ~m$
At t = 4 s:
$x=16 ~m+10 ~m$
$x=26 ~m$
