Sidney P. answered • 06/12/20
Astronomy, Physics, Chemistry, and Math Tutor
This situation has both centripetal acceleration ac and tangential acceleration aT. The first is easy: ac = v2/r. Halfway through the turn, the speed is 80 km/hr which converts to 22.22 m/s. This gives ac = 32.92 m/s2.
For aT use kinematics: vf2 = vi2 + 2ax. In this case I believe that the displacement x would be 1/2(2πr) = 15π = 47.1 m, for the motion around a semicircle while the speed is changing from 29.2 to 15.3 m/s. Then aT = (15.32 - 29.22) / (2 * 47.1) = -6.55 m/s2. [This may be wrong because, although the magnitude of the acceleration is constant, the direction keeps changing, and the kinematic equation is for constant a.]
Total acceleration comes from adding the two components perpendicular to each other via a2 = ac2 + aT2 which yields a = 33.6 m/s.
Sidney P.
but I already did 1/2 of the circumference for X: 15 pi instead of 30 pi.06/13/20
Rajai A.
The velocity 29.2 m/s is the initial , 15.3 m/s is the final velocity, for the complete turn ,not for half turn.this what i can understand from the question .06/13/20
Sidney P.
From the wording of the question, it is clear to me that the car begins a semi-circular path at 105 km/h [29.2 m/s] and ends the semi-circle, not the whole circle, at 55 km/h [15.3 m/s].06/13/20
Rajai A.
You are completely right.06/15/20
Rajai A.
Hi Thank you X = 2.pi .r for the full turn So (a) will be half the -6.55 a( tang ) will be - 3.28 m/s206/13/20