Answer
(a) $0.25~s$
(b) $110~m/s^2$
(c) Heigth: $0.55~m$
Speed: $11~m/s$
Work Step by Step
(a) $v_{av}=\frac{v+v_0}{2}=\frac{26.0~m/s+0}{2}=13.0~m/s$
$v_{av}=\frac{\Delta x}{\Delta t}$. Rearrange the equation:
$\Delta t=\frac{\Delta x}{v_{av}}=\frac{3.2~m}{13.0~m/s}=0.25~s$
(b) $v^2=v_0^2+2a\Delta x$
$(26.0~m/s)^2=0^2+2a(3.2~m)$
$a=\frac{676~m^2/s^2}{6.4~m}=110~m/s^2$
(c) Put the origin at the starting position: $x_0=0$
$x=x_0+v_0t+\frac{1}{2}at^2$.
$x=0+0(0.10~s)+\frac{1}{2}(110~m/s^2)(0.10~s)^2$
$x=0.55~m$
$v=v_0+at=0+(110~m/s^2)(0.10~s)=11~m/s$
