Kinematics - Interpreting Graphs and deriving equations

In summary, the shortest road distance from Toronto City Hall to the Shaw festival theatre in Niagara-on-the-Lake is 131 km. The total distance travelled by the truck is 130 km in 2 hours, with an average speed of 65 km/h. This means that the truck has almost reached the festival theatre.
  • #1
alexandria
169
2

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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  • #3
Thanks :)
 

1. What is kinematics?

Kinematics is the branch of physics that studies the motion of objects without considering the forces that cause the motion.

2. How do you interpret a motion graph?

A motion graph shows the relationship between an object's position, velocity, and acceleration over time. The slope of the line on a position-time graph represents the object's velocity, while the slope of the line on a velocity-time graph represents the object's acceleration.

3. How can you derive equations from a motion graph?

To derive equations from a motion graph, you can use the slope formula (m = Δy/Δx) to find the slope of the line at different points on the graph. The slope of the position-time graph will give you the velocity equation (v = Δx/Δt), and the slope of the velocity-time graph will give you the acceleration equation (a = Δv/Δt).

4. What is the difference between average and instantaneous velocity?

Average velocity is the total displacement of an object divided by the total time taken. Instantaneous velocity is the velocity of an object at a specific moment in time. It is calculated by finding the slope of the tangent line to the position-time graph at that point.

5. How can you use kinematics to solve real-world problems?

Kinematics can be used to solve real-world problems by analyzing an object's motion and using equations to determine its position, velocity, and acceleration at different points in time. This information can be used to make predictions about an object's future motion or to calculate important factors such as distance traveled, speed, or acceleration. It is also used in engineering and technology to design and optimize machines and structures.

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