1. Define die term scalar 2. Calculate the total time it takes the coach to walk from A to D . 3. Calculate the total distance the coach has walked from A to D . 4. Determine the DISPLACEMENT of the coach from A to D by means of an accurate CONSTRUCTION of the different vectors in which you use the tail-to-head method. Use a scale where 1 cm represents 10 m 5. Calculate the average speed of the coach between A and D . 6. Convert the speed you have calculated in question 2.1 .5 to km . $$ \mathrm{h}^{-1} $$ 7. How does the magnitude of the coach's average velocity between A and D compare with his average speed between A and D ? Write down only GREATER THAN, LESS THAN or SAME AS. 8. Explain your answer in question 7 without doing a calculation. 9. Define the term displacement.

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1. A scalar is a physical quantity that has magnitude only, with no associated direction.

2. Let the coach’s walking times for each segment be $$ t_1 $$, $$ t_2 $$, and $$ t_3 $$. Then the total time is given by  
$$
T = t_1 + t_2 + t_3.
$$
(Substitute the given times in order to obtain a numerical value.)

3. If the distances covered on each segment are $$ d_1 $$, $$ d_2 $$, and $$ d_3 $$, then the total distance is  
$$
D_{\text{total}} = d_1 + d_2 + d_3.
$$
(Again, use the provided distances to calculate the total.)

4. To determine the displacement from point A to point D, construct the vectors corresponding to each segment on a diagram using the tail-to-head method. The displacement vector $$\vec{d}$$ is the resultant vector from the starting point A directly to the final point D. Once drawn on your diagram, measure its length in centimeters and convert to meters using the given scale:  
$$
\text{Actual Displacement (in m)} = (\text{Measured length in cm}) \times 10.
$$

5. The average speed is calculated by dividing the total distance by the total time. That is,  
$$
\text{Average Speed} = \frac{D_{\text{total}}}{T}.
$$
(Ensure that the distance is in meters and the time is in seconds when performing the calculation.)

6. To convert the average speed to kilometers per hour, if the speed in meters per second is $$ v $$, then  
$$
v_{\text{km/h}} = v \times 3.6.
$$
(Alternatively, if your calculated speed is in another unit, convert appropriately so that the final unit is $$\mathrm{km\,h^{-1}}$$.)

7. The magnitude of the coach's average velocity is  
$$
\text{LESS THAN}
$$
his average speed.

8. The reason is that the average speed is based on the total path length traveled, while the magnitude of the average velocity is based solely on the straight-line (shortest) distance between points A and D. Since the path is not a straight line, the displacement (and hence the average velocity) is less than the total distance traveled.

9. Displacement is a vector quantity that represents the change in position of an object. It is defined as the straight-line distance from an object’s initial position to its final position, along with the direction from the start to the end point.
1. A scalar is a quantity with only size, no direction. 2. Total time from A to D is the sum of the time for each part of the walk. 3. Total distance from A to D is the sum of the distances walked in each part. 4. Draw vectors for each part of the walk using the tail-to-head method, then measure the displacement vector's length on the diagram and convert it to meters using the scale. 5. Average speed is total distance divided by total time. 6. Convert the speed from meters per second to kilometers per hour by multiplying by 3.6. 7. The magnitude of average velocity is LESS THAN the average speed. 8. This is because average speed considers the total path length, while average velocity only considers the straight-line distance between the start and end points. 9. Displacement is the straight-line distance and direction from the starting point to the ending point.

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