Physics: Scalars and Measurements

Use the equations: the horizontal component is found by multiplying the vector's magnitude by cosθ, and the vertical component by sinθ.

The vector sum of the first two forces equals the magnitude and opposite direction of the third force, maintaining equilibrium.

Velocity is the rate of change of displacement, represented as displacement divided by time, and is a vector quantity measured in m/s.

<p>Distance is the total path length traveled regardless of direction, while displacement is the shortest straight-line distance between two points with a defined direction.</p> Signup and view all the answers

<p>The slope of a displacement-time graph represents velocity.</p> Signup and view all the answers

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

<p>Acceleration is calculated using the equation a = (v - u)/t, which gives a = (36 - 0)/9 = 4 m/s².</p> Signup and view all the answers

<p>A vector can be resolved into its components by using trigonometric ratios, specifically sin and cos, based on the angle it makes with the horizontal.</p> Signup and view all the answers

<p>The displacement is calculated using the equation s = ut + ½at².</p> Signup and view all the answers

<p>The relationship is given by the equation v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.</p> Signup and view all the answers

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

<p>The total distance can be determined by calculating the area under the velocity-time graph.</p> Signup and view all the answers

<p>The slope of a velocity-time graph represents the acceleration of the object.</p> Signup and view all the answers

<p>Time taken can be calculated by dividing the number of spaces on the ticker tape by the frequency of the ticker timer: $t = \frac{n}{f}$.</p> Signup and view all the answers

<p>The slope should be adjusted to ensure the trolley moves at a constant velocity, reducing acceleration due to external forces.</p> Signup and view all the answers

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

<p>The resultant can be calculated by using vector addition, often visualized through graphical methods such as the parallelogram law.</p> Signup and view all the answers

<p>The distance can be calculated using the area under the velocity-time graph, which includes both the acceleration and constant speed phases.</p> Signup and view all the answers

<p>Her acceleration is $a = \frac{(10 - 0)}{3} = \frac{10}{3} \approx 3.33 , \text{m/s}^2$.</p> Signup and view all the answers

<p>Oiling the trolley's wheels reduces friction, allowing for smoother motion and more accurate measurements.</p> Signup and view all the answers

<p>Scalar quantities are physical quantities 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>An example of a vector quantity is velocity.</p> Signup and view all the answers

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

<p>Pythagoras' theorem is used to calculate the hypotenuse when vectors are perpendicular.</p> Signup and view all the answers

<p>The resultant vector is the single vector that results from the vector sum of two or more vectors.</p> Signup and view all the answers

<p>'SOHCAHTOA' is a mnemonic used to remember the relationships in right-angled triangles for trigonometric functions.</p> Signup and view all the answers

<p>Time is typically measured using a stopwatch or electronic timer.</p> Signup and view all the answers

<p>Displacement is the shortest distance from the initial to the final position, having both magnitude and direction.</p> Signup and view all the answers

<p>To calculate acceleration, first measure the initial and final velocities, then determine the time taken using the formula $t = \frac{n}{f}$, and finally use the formula $a = \frac{v - u}{t}$.</p> Signup and view all the answers

<p>The total distance is calculated by finding the area under the velocity-time graph, which can be expressed as the sum of the areas of geometric shapes formed.</p> Signup and view all the answers

<p>Even spacing indicates the trolley is moving at constant velocity, which minimizes errors in measuring distance and improves accuracy in calculating velocity.</p> Signup and view all the answers

<p>The runway must be sloped appropriately, the trolley should be released without external forces, and friction should be minimized for uniform acceleration.</p> Signup and view all the answers

<p>Sketch the graph with velocity on the y-axis and time on the x-axis, representing uniform acceleration and constant velocity; calculate the area under the graph to find the distance.</p> Signup and view all the answers

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

<p>A vector quantity has both magnitude and direction.</p> Signup and view all the answers

<p>The resultant vector is calculated using Pythagoras' theorem, where the hypotenuse represents the resultant and the two other sides are the vector components.</p> Signup and view all the answers

<p>The direction of the resultant vector is determined by the direction of the larger vector if vectors are in opposite directions, while in the same direction, it points in that direction.</p> Signup and view all the answers

<p>They allow for accurate measurements of small distances, providing precise values that enhance the quality of experimental data.</p> Signup and view all the answers

<p>Speed is calculated by dividing the distance traveled by the time taken, expressed as $v = \frac{d}{t}$.</p> Signup and view all the answers

<p>The resultant is found by simply adding the magnitudes of the two forces, $R = F_1 + F_2$.</p> Signup and view all the answers

<p>Angles are used to determine the components of the vectors, allowing for accurate calculation of the resultant using trigonometric functions.</p> Signup and view all the answers

<p>Pressure is defined as the force applied per unit area, and it has magnitude but no direction.</p> Signup and view all the answers

<p>Speed is a scalar quantity representing how fast an object moves, while velocity is a vector quantity that includes direction.</p> Signup and view all the answers

<p>The direction of the components is determined by the angle with respect to the hypotenuse, where the adjacent component corresponds to the cosine and the opposite component corresponds to the sine of the angle.</p> Signup and view all the answers

<p>Both magnitude and direction are essential as vectors are defined by both, ensuring that resultant values accurately represent the combined effects of forces or displacements.</p> Signup and view all the answers

<p>Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides, expressed as $c^2 = a^2 + b^2$.</p> Signup and view all the answers

<p>Average velocity is calculated by dividing displacement by the total time taken, expressed as $v = \frac{s}{t}$.</p> Signup and view all the answers

<p>Equilibrium occurs when all forces in the system are balanced, meaning the vector sum of the forces equals zero, indicating stability in the system.</p> Signup and view all the answers

<p>The area under a velocity-time graph represents the distance traveled during the time interval, calculated as the sum of the areas of rectangles and triangles.</p> Signup and view all the answers

<p>Acceleration is defined as the rate of change of velocity over time, calculated as $a = \frac{\Delta v}{t}$.</p> Signup and view all the answers

<p>Displacement is the vector quantity representing the shortest straight-line distance between two points, while distance is the total path length traveled, irrespective of direction.</p> Signup and view all the answers

<p>The slope of a distance-time graph represents velocity, calculated as the change in distance over the change in time, expressed as $v = \frac{\Delta s}{\Delta t}$.</p> Signup and view all the answers

<p>'Tip to tail' means arranging vectors so that the tail of one vector is placed at the tip of the previous vector to visually determine the resultant vector.</p> Signup and view all the answers