The coordinate axes of the reference frame S′ remain parallel to those of S, as S′ moves away from S at a constant velocity v⃗ SS′=(4.0iˆ+3.0jˆ+5.0kˆ)m/s. (a) If at time t = 0 the origins coincide, what is the position of the origin O′ in the S frame as a function of time? (b) How is particle position for r⃗ (t) and r⃗ ′(t), as measured in S and S′, respectively, related? (c) What is the relationship between particle velocities v⃗ (t)andv⃗ ′(t)? (d) How are accelerations a⃗ (t)anda⃗ ′(t) related?

An ideal otto cycle has a compression ratio of 8. at the beginning of the compression process, air is at 95 kpa and 27°c, and 750 kj/kg of heat is transferred to air during the constant-volume heat-addition process. assuming constant specific heats at room temperature, determine (a) the pressure and temperature at the end of the heat-addition process, (b) the net work output, (c) the thermal efficiency, and (d) the mean effective pressure for the cycle. (4390 kpa, 1730 k; 423 kj/kg; 56.4%; 534 kpa)