Answer
(a) $x = 6.0~m$
(b) $v = 2.0~m/s$
(c) $a = -2.0~m/s^2$
Work Step by Step
(a) The area between the velocity versus time graph and the x-axis is equal to the displacement.
The area under the curve from t = 0 to t = 2 is $\frac{6+2}{2.0}*2$ (because it is a trapezoid.)
$\Delta x = 8.0~m$
$x = x_0+\Delta x$
$x = 2.0 + 8.0~m$
$x = 10.0~m$
(b) We can read the value of the velocity directly from the graph. Therefore,
$v = 2.0~m/s$
(c) The acceleration is equal to the slope of the velocity versus time graph. Therefore,
$a = \frac{-6.0~m/s}{3.0~s} = -2.0~m/s^2$
