(Solved): Class worksheet: Kinematics in One Dimension Kinematic equations: \[ \begin{array}{l} v_{i}=v_{i}+a ...

Class worksheet: Kinematics in One Dimension Kinematic equations: \[ \begin{array}{l} v_{i}=v_{i}+a_{n} \Delta t \\ s_{f}=s_{i}+v_{i t} \Delta t+\frac{1}{2} a_{i}(\Delta t)^{2} \\ v_{f i}^{2}=v_{i}^{2}+2 a_{i} \Delta s \end{array} \] 1. The Rogue River in Oregon is so rocky in spots that jet boats become a popular way for tourists to see wild stretches of the river. A system of air jets thrusting downward keep the boat suspended above the water and a second system of air jets move it horizontally. A jet boat driver comes around a bent in the river moving due west at a speed of \( 12 \mathrm{~m} / \mathrm{s} \) when she discovers that a large Douglas fir tree has fallen across the river 20 meters in front of her. She quickly reverses her horizontal jets so that they deliver a constant acceleration in an easterly direction. The jet boat slows down considerably and reaches the log affer \( 2.5 \) seconds What is its acceleration? Does it stop in time? If not, bow fast is it going when it hits the log? A) Draw a motion diagram and list all known values: B) Sketch the position, velocity anflocceleration versus time graphs. Position-time graph Velocity-time graph Acceleration-time graph C) Solution: \[ S_{f}=S_{i}+v_{i s} \Delta t+\frac{1}{2} \theta_{s}(\Delta t)^{2} . \] \( \Delta t=2.5 \mathrm{~s} \) \[ \begin{array}{ll} S_{f}=0 \mathrm{~m} & 10=\frac{1}{2} a_{s}(6.25) \\ S_{i}=20 \mathrm{~m} & 1.6=\frac{1}{2} a_{s} \\ 3.2=a_{5} \end{array} \]