Sure, let’s break this down step-by-step to solve the given question.
First, we will plot the distance-time graph based on the given values:
### i) Draw a distance-time graph of the motion:
We are given the following data points from the table:
- [tex]\( (t = 0\, s, s = 0\, m) \)[/tex]
- [tex]\( (t = 10\, s, s = 4\, m) \)[/tex]
- [tex]\( (t = 20\, s, s = 8\, m) \)[/tex]
- [tex]\( (t = 30\, s, s = 12\, m) \)[/tex]
- [tex]\( (t = 40\, s, s = 16\, m) \)[/tex]
- [tex]\( (t = 50\, s, s = 20\, m) \)[/tex]
1. Create a Cartesian coordinate system with the x-axis representing time ([tex]\( t \)[/tex]) in seconds and the y-axis representing distance ([tex]\( s \)[/tex]) in meters.
2. Plot each of the given points on the graph.
3. Connect the plotted points with a smooth line since the motion is uniform.
The resulting graph should show a straight line due to uniform acceleration (constant increase in distance over equal time intervals).
### ii) Determine from the graph the distance covered by the body after 4.5 seconds:
To find the distance covered after 4.5 seconds, we need to use interpolation since 4.5 seconds does not directly appear on our list of time values.
1. Look closely at the provided graph and see the relation between time and distance. The graph should be linear, meaning each increase in time interval corresponds to a proportional increase in distance, also maintaining uniform acceleration.
2. Since the time 4.5 seconds is between the intervals 0 and 10 seconds, interpolate the distance accordingly. Graphically estimate the point corresponding to 4.5 seconds on the x-axis and then see where it intersects the plotted line to read off the corresponding distance value on the y-axis.
However, without the actual graph, let's calculate it using the data points.
Using linear interpolation between (0, 0) and (10, 4):
The formula for interpolation is:
[tex]\[ s = s_1 + \left( \frac{t - t_1}{t_2 - t_1} \right) (s_2 - s_1) \][/tex]
Where:
- [tex]\( (t_1, s_1) = (0, 0) \)[/tex]
- [tex]\( (t_2, s_2) = (10, 4) \)[/tex]
[tex]\[ s = 0 + \left( \frac{4.5 - 0}{10 - 0} \right) (4 - 0) \][/tex]
[tex]\[ s = 0 + \left( \frac{4.5}{10} \right) \times 4 \][/tex]
[tex]\[ s = 0 + 0.45 \times 4 \][/tex]
[tex]\[ s = 1.8 \][/tex]
So, after 4.5 seconds, the distance covered by the body is 1.8 meters.
### Conclusion
The distance covered by the body after 4.5 seconds is 1.8 meters. This estimation can better visualize and confirm it by plotting on the distance-time graph.
