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Questions and Answers
What is indicated by the area under a velocity-time graph and how is it calculated?
The area under a velocity-time graph represents the distance travelled during a time interval, calculated as the sum of the areas of rectangles and triangles.
Describe how the direction of the resultant vector changes when adding two vectors that are in opposite directions.
When adding two vectors in opposite directions, the direction of the resultant vector is determined by the larger vector.
Explain what 'tip to tail' means in the context of vector addition.
'Tip to tail' refers to arranging vectors such that the tail of one vector is placed at the tip of the previous vector, allowing for the visual determination of the resultant vector.
Using the equation for constant acceleration, find the acceleration of a body that starts from rest and reaches 36 m/s in 9 seconds.
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What formula is used to calculate the displacement of a body under uniform acceleration and what do the terms represent?
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Study Notes
Velocity-Time Graph
- The area beneath a velocity-time graph signifies the total distance traveled over a specific time interval.
- Calculation involves summing the areas of rectangles and triangles formed on the graph.
Displacement-Time Graph
- The slope of a displacement-time graph indicates the object's velocity, with steeper slopes representing greater speeds.
Resultant Vector Direction
- When adding vectors in opposite directions, the resultant vector’s direction aligns with the larger vector.
- For vectors in the same direction, the resultant vector also points in that unified direction.
Tip to Tail Method
- The 'tip to tail' method in vector addition entails positioning the tail of one vector at the tip of the preceding vector to visually calculate the resultant vector.
Perpendicular Components of a Vector
- To determine a vector's perpendicular components from the hypotenuse and angle:
- The horizontal component is found through: horizontal = magnitude × cos(θ).
- The vertical component is calculated by: vertical = magnitude × sin(θ).
Calculating Acceleration
- Acceleration for a body starting from rest (initial velocity u = 0) and reaching a speed of 36 m/s in 9 seconds is given by:
- Formula: ( a = \frac{(v - u)}{t} )
- Calculation yields: ( a = \frac{(36 - 0)}{9} = 4 , m/s² ).
Displacement with Uniform Acceleration
- Displacement of an object under uniform acceleration is computed using:
- Formula: ( s = ut + \frac{1}{2} at² )
Initial and Final Velocity in Constant Acceleration
- The relationship between initial velocity (u), final velocity (v), acceleration (a), and time (t) is represented by:
- Equation: ( v = u + at )
Pythagoras' Theorem in Vector Addition
- Pythagoras' theorem aids in finding the hypotenuse length when dealing with perpendicular vectors, ensuring accurate vector addition.
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Description
Test your understanding of key concepts in calculating areas and slopes in velocity-time and displacement-time graphs. This quiz covers essential physics principles related to vectors and their resultant directions. Perfect for reinforcing your knowledge before exams!
