Physics: Physical Quantities and Scalars

The perpendicular components can be found using trigonometric functions: multiply the hypotenuse by sinθ for the vertical component and cosθ for the horizontal component.

Drawing the vectors 'tip to tail' helps visualize the relationship between the two vectors, allowing the resultant vector to be determined as the line drawn from the tail of the first vector to the tip of the second.

Displacement represents the shortest straight-line distance between two points, including direction, while distance traveled is the total length of the path taken regardless of direction.

<p>Acceleration is the rate of change of velocity, measured in meters per second squared (m/s²).</p> Signup and view all the answers

<p>The resultant vector is a single vector that represents the combined effect of multiple vectors, while the components are the parts into which the original vector is broken down to analyze its effects in perpendicular directions.</p> Signup and view all the answers

<p>Acceleration can be calculated using the formula $a = \frac{(v - u)}{t}$, resulting in $a = \frac{(36 - 0)}{9} = 4 \text{ m/s}^2$.</p> Signup and view all the answers

<p>Average velocity is the rate of change of displacement and can be calculated as $rac{displacement}{time}$, measured in meters per second (m/s).</p> Signup and view all the answers

<p>The slope of a velocity-time graph represents acceleration, calculated as $rac{(v - u)}{t}$.</p> Signup and view all the answers

<p>The area under a velocity-time graph represents the distance traveled during that time interval.</p> Signup and view all the answers

<p>The acceleration would be calculated as $a = \frac{(v - u)}{t}$, resulting in $a = \frac{(25 - 0)}{5} = 5 \text{ m/s}^2$.</p> Signup and view all the answers

<p>The formula for acceleration is $a = \frac{v - u}{t}$, where $v$ is the final velocity, $u$ is the initial velocity, and $t$ is the time taken.</p> Signup and view all the answers

<p>The time is measured by dividing the number of spaces between dots on the ticker tape by the frequency of the ticker timer, using the formula $t = \frac{n}{f}$.</p> Signup and view all the answers

<p>The slope ensures that the trolley accelerates freely under the influence of gravity, providing a constant acceleration throughout the motion.</p> Signup and view all the answers

<p>The distance is calculated as the area under the velocity-time graph, which can be determined using the formula for the area of triangles and rectangles.</p> Signup and view all the answers

<p>Vector quantities have both magnitude and direction, such as velocity, while scalar quantities have only magnitude, like distance.</p> Signup and view all the answers

<p>The stopping time can be calculated using $t = \frac{v}{a} = \frac{16}{2.5} = 6.4$ seconds.</p> Signup and view all the answers

<p>To convert to km/h, multiply by 3.6: $330 \times 3.6 = 1188$ km/h.</p> Signup and view all the answers

<p>The horizontal component is found using $v_x = v \cos(\theta)$ and the vertical component using $v_y = v \sin(\theta)$, where $ heta$ is the angle.</p> Signup and view all the answers

<p>The magnitude is calculated using $v = \sqrt{(8.2^2 + 3.7^2)} \approx 9.4$ m/s and the direction can be found with $\tan^{-1}(\frac{3.7}{8.2}) \approx 24.6°$ north of east.</p> Signup and view all the answers

<p>Scalar quantities are measurable values that have only magnitude and no direction.</p> Signup and view all the answers

<p>Vernier calipers and micrometers are used to measure small distances.</p> Signup and view all the answers

<p>Speed is the distance traveled per unit time.</p> Signup and view all the answers

<p>Velocity is an example of a vector quantity.</p> Signup and view all the answers

<p>The resultant vector is found by subtracting the smaller vector from the larger one and taking the direction of the larger vector.</p> Signup and view all the answers

<p>The length of an arrow represents the magnitude of the vector.</p> Signup and view all the answers

<p>Pythagoras’ theorem is used to calculate the hypotenuse.</p> Signup and view all the answers

<p>Vectors acting in the same direction are simply added together.</p> Signup and view all the answers

<p>SOHCAHTOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent.</p> Signup and view all the answers

<p>The SI unit of distance is the meter (m).</p> Signup and view all the answers

<p>Vector quantities have both magnitude and direction, whereas scalar quantities only have magnitude.</p> Signup and view all the answers

<p>Trigonometry is used with Pythagoras’ theorem to calculate the hypotenuse, and sine, cosine, or tangent functions to determine the respective sides.</p> Signup and view all the answers

<p>A meter stick is used to measure distance, providing a standard unit of measurement in meters.</p> Signup and view all the answers

<p>The resultant vector can be calculated using Pythagoras' theorem, where the resultant is the square root of the sum of the squares of the two perpendicular vectors.</p> Signup and view all the answers

<p>In vector quantities, direction significantly affects the outcome, like force direction impacting movement, while scalar quantities like speed only consider magnitude.</p> Signup and view all the answers

<p>The components can be found by using trigonometric functions, specifically $v_{x} = v \cdot \cos(\theta)$ for the east component and $v_{y} = v \cdot \sin(\theta)$ for the north component.</p> Signup and view all the answers

<p>The vector sum of the first two forces equals the magnitude and opposite direction of the third force, maintaining equilibrium in the system.</p> Signup and view all the answers

<p>Pythagoras' Theorem allows us to calculate the magnitude of the resultant vector when two vectors are perpendicular, using the formula $R = \sqrt{A^2 + B^2}$.</p> Signup and view all the answers

<p>Average velocity is calculated using the formula $v_{avg} = \frac{displacement}{time}$, expressed in meters per second (m/s).</p> Signup and view all the answers

<p>Acceleration is the rate of change of velocity, calculated as $a = \frac{(v - u)}{t}$, where $v$ is final velocity, $u$ is initial velocity, and $t$ is time.</p> Signup and view all the answers

<p>Scalar quantities have only magnitude, while vector quantities have both magnitude and direction.</p> Signup and view all the answers

<p>To find the resultant vector at an angle, you can use Pythagoras’ theorem and trigonometric functions to calculate its magnitude and direction.</p> Signup and view all the answers

<p>The measurement of time is crucial because speed is defined as the distance traveled per unit time.</p> Signup and view all the answers

<p>The direction is critical because the resultant vector is determined by subtracting the magnitudes of the opposing vectors.</p> Signup and view all the answers

<p>The SI unit meters provides a standard measurement for distance, ensuring consistency and accuracy in scientific calculations.</p> Signup and view all the answers