Kinematics - Interpreting Graphs and deriving equations

AI Thread Summary
The discussion focuses on calculating the distance and average speed of a transport journey from Toronto City Hall to the Shaw Festival Theatre, which is 131 km away. The user calculates the distance traveled at different speeds over specified time intervals, totaling 130 km in 2 hours. The average speed is then determined to be 65 km/h. The calculations are confirmed as correct by another participant. The thread emphasizes understanding kinematics through graph interpretation and equation derivation.
alexandria
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Homework Statement


upload_2016-3-21_23-15-23.png


Homework Equations


average speed = total distance/total time

The Attempt at a Solution



24. [/B]

The shortest road distance from Toronto City Hall to the Shaw festival theatre in Niagara-on-the-Lake is 131 km.

a)

First I will calculate the area of each rectangle using this formula: A = l x w

d = (40 km/h) (0.5 h)

= 20 km

d = (80 km/h) (1.0 h)

= 80 km

d = (60 km/h) (0.5 h)

= 30 km

Total distance travelled:

total d = 20 km + 80 km + 30 km

total d = 130 km

We already know that the shortest road distance from Toronto City Hall to the Shaw festival theatre is 131 km. In 2 hours, the transport has traveled a total of 130 km, meaning it has just about reached the festival theatre.

b)

Average speed of the truck = total distance / total time

= 130 km / 2.0 h

= 65 km/h
please verify if my answer is correct.
thank you :)
 

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Looks right.
 
Thanks :)
 
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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