Awild ride a car in a roller coaster moves along a track that consists of a sequence of ups and downs. let the x axis be parallel to the ground and the positive y axis point upward. in the time interval from t=0 to t=4 s, the trajectory of the car along a certain section of the track is given by r⃗ =a(1m/s)ti^+a[(1m/s3)t3−6(1m/s2)t2] j^, where a is a positive dimensionless constant.

solution:

write the coordinates of the points A and B  

A= (0,0,14)ft

B= (5,-6,0)ft

write the position vector of a with recpect to b

R_{BA}=(0-5)i+(0-(-6))j+(14-0)k

     =-5i+6k+14k

calculation of a magnitude of the vector R_{BA}

\left | R_{BA} \right |=\sqrt{(-5)^2+6^2+14^2}

                      =\sqrt{25+36+196}

                      =16.031ft

calculation of the unit vector  

\frac{-5i+6k+14k}{16.031}

calculation of the force

F_{BA}=R_{BA}U_{BA}  

here, F_{BA} is the magnitude of the force.

substitute 350lb for F_{BA} and (\frac{-5i+6k+14k}{16.031}) for U_{BA}.

F_{BA} = 350 x (\frac{-5i+6k+14k}{16.031})

      =-109.2i+131j+305.7k lb

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

are there options? cause you ain’t. real specific