if a truck moving at 4 m/s towards south takes a turn towards east causing change in velocity =3 m/s. If turning time = 10 s then find average acceleration.
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Answers
Answer:
Explanation:
If a truck moving at 4 m/s towards the south takes a turn around towards the east, its velocity changes to 3m/s. If the turning time is 10 seconds, what is the average acceleration of the truck?
This question requires you to consider both velocity and acceleration as vectors. If we align cartesian co-ordinates with the compass so that north is in the x direction and east in the y direction then the starting velocity is (−4,0) m/s and the finishing velocity is (0,3) m/s. The acceleration is velocity change divided by time, so this is:
110((0,3)−(−4,0))=(0.4(N),0.3(E)) m/s2
This answer is valid as it is, but it’s often more useful to consider the size and direction rather than x,y values. The size of the acceleration by Pythagoras is:
0.42+0.32−−−−−−−−−√=0.5 m/s2
and the direction is
arctan(0.30.4)≈37˚ compass bearing
which is around 8˚ north of NE. Note that the truck driver will experience a centrifugal acceleration of the same size but opposite direction to this, so they would feel pushed in a direction of 37+180=217˚ , which of course is 8˚ south of SW.