Answer
(a) $5.2~m$
(b) $2.6~m$
(c) $2.6~m/s$
Work Step by Step
Constant-acceleration motion:
$v_{av}=\frac{v_0+v}{2}$
And $v_{av}=\frac{\Delta x}{\Delta t}$. Rearranging the equation:
$\Delta x=(v_{av})(\Delta t)$
- From $0$ to $4~s$:
$v_{av}=\frac{v_0+v}{2}=\frac{0+V}{2}=\frac{V}{2}$
$\Delta x_1=(v_{av})(\Delta t)=\frac{V}{2}(4~s)=V(2~s)$
- From $4~s$ to $6~s$:
$v_{av}=\frac{v_0+v}{2}=\frac{V+V}{2}=V$
$\Delta x_2=(v_{av})(\Delta t)=V(2~s)$
- From $6~s$ to $8~s$:
$v_{av}=\frac{v_0+v}{2}=\frac{V+0}{2}=\frac{V}{2}$
$\Delta x_3=(v_{av})(\Delta t)=\frac{V}{2}(2~s)=V(1~s)$
Now: $\Delta x_1+\Delta x_2+\Delta x_3=13~m$
$V(2~s)+V(2~s)+V(1~s)=13~m$
$V(5~s)=13~m$
$V=\frac{13~m}{5~s}=2.6~m/s$
(a) $\Delta x_1=V(2~s)=(2.6~m/s)(2~s)=5.2~m$
(b) $\Delta x_3=V(1~s)=(2.6~m/s)(1~s)=2.6~m$
(c) $V=2.6~m/s$
