0.2 Motion in one dimension  (Page 10/16)

This means that Lesedi has a displacement of $100\mathrm{m}$ towards his house.

Velocity and acceleration

1. Use the graphs in [link] to calculate each of the following:
   1. Calculate Lesedi's velocity between $50\mathrm{s}$ and $100\mathrm{s}$ using the $x$ vs. $t$ graph. Hint: Find the gradient of the line.
   2. Calculate Lesedi's acceleration during the whole motion using the $v$ vs. $t$ graph.
   3. Calculate Lesedi's displacement during the whole motion using the $v$ vs. $t$ graph.
2. Thandi takes $200\mathrm{s}$ to walk $100\mathrm{m}$ to the bus stop every morning. In the evening Thandi takes $200\mathrm{s}$ to walk $100\mathrm{m}$ from the bus stop to her home.
   1. Draw a graph of Thandi's position as a function of time for the morning (assuming that Thandi's home is the reference point). Use the gradient of the $x$ vs. $t$ graph to draw the graph of velocity vs. time. Use the gradient of the $v$ vs. $t$ graph to draw the graph of acceleration vs. time.
   2. Draw a graph of Thandi's position as a function of time for the evening (assuming that Thandi's home is the origin). Use the gradient of the $x$ vs. $t$ graph to draw the graph of velocity vs. time. Use the gradient of the $v$ vs. $t$ graph to draw the graph of acceleration vs. time.
   3. Discuss the differences between the two sets of graphs in questions 2 and 3.

Experiment : motion at constant velocity

Aim:

Apparatus:

Method

1. Work with a friend. Copy the table below into your workbook.
2. Complete the table by timing the car as it travels each distance.
3. Time the car twice for each distance and take the average value as your accepted time.
4. Use the distance and average time values to plot a graph of “Distance vs. Time" onto graph paper . Stick the graph paper into your workbook. (Remember that “A vs. B" always means “y vs. x").
5. Insert all axis labels and units onto your graph.
6. Draw the best straight line through your data points.
7. Find the gradient of the straight line. This is the average velocity.

Results:

Conclusions:

1. Did the car travel with a constant velocity?
2. How can you tell by looking at the “Distance vs. Time" graph if the velocity is constant?
3. How would the “Distance vs. Time" look for a car with a faster velocity?
4. How would the “Distance vs. Time" look for a car with a slower velocity?

Motion at constant acceleration

The final situation we will be studying is motion at constant acceleration. We know that acceleration is the rate of change of velocity. So, if we have a constant acceleration, this means that the velocity changes at a constant rate.

Let's look at our first example of Lesedi waiting at the taxi stop again. A taxi arrived and Lesedi got in. The taxi stopped at the stop street and then accelerated as follows: After $1\mathrm{s}$ the taxi covered a distance of $\mathrm{2,5}\mathrm{m}$ , after $2\mathrm{s}$ it covered $10\mathrm{m}$ , after $3\mathrm{s}$ it covered $\mathrm{22,5}\mathrm{m}$ and after $4\mathrm{s}$ it covered $40\mathrm{m}$ . The taxi is covering a larger distance every second. This means that it is accelerating.