4 questions about distance travelled and magnitude of displacement

AI Thread Summary
Total distance traveled can equal the magnitude of displacement when movement occurs in a straight line without changing direction. However, total distance can exceed displacement, as illustrated by moving north 20 units and then south 30 units, resulting in a distance of 50 units and a displacement of 10 units. The magnitude of displacement cannot exceed total distance traveled because displacement measures the shortest path between two points, while distance accounts for the entire path taken. Average speed can equal the magnitude of average velocity only in scenarios where motion occurs in a straight line without any changes in direction. Understanding these concepts is crucial for solving related physics problems effectively.
Kelan
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Homework Statement


1. is it possible for the total distance traveled to equal the magnitude of the displacement? if "no" why not? if "yes" give an example

2. is it possible for the total distance traveled to exceed the magnitude of the displacement? if "no" why not? if "yes" give an example

3.is it possible for the magnitude of the displacement to exceed the total distance travelled? if "no" why not? if "yes" give an example

4. can the average speed ever equal the magnitude of the average velocity? if "no" why not? if "yes" give an example

Thanks in advance, Kelan

Homework Equations





The Attempt at a Solution



ok so i know that the magnitude can not be greater then the distance traveled but i do not know why i need it explained to me i only know this because the teacher told us
 
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You need to make an attempt at answering.
 
Are you not going to have a go yourself first?
 
try thinking about the difference between displacement and distance and come up with scenario's that will help you answer the question.
 
1. If you travel in a straight line...then yes. Both can be the same.

2. Yes, go north 20, go south 30. Your displacement is 10 and your distance is 50.

you can do the rest.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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