0.2 Motion in one dimension  (Page 6/16)

Differences between speed and velocity

The differences between speed and velocity can be summarised as:

Additionally, an object that makes a round trip, i.e. travels away from its starting point and then returns to the same point has zero velocity but travels a non-zero speed.

Displacement and related quantities

1. Theresa has to walk to the shop to buy some milk. After walking $100\mathrm{m}$ , she realises that she does not have enough money, and goes back home. If it took her two minutes to leave and come back, calculate the following:
   1. How long was she out of the house (the time interval $\Delta t$ in seconds)?
   2. How far did she walk (distance (D))?
   3. What was her displacement ( $\Delta x$ )?
   4. What was her average velocity (in m $·$ s ${}^{-1}$ )?
   5. What was her average speed (in m $·$ s ${}^{-1}$ )?

   

2. Desmond is watching a straight stretch of road from his classroom window. He can see two poles which he earlier measured to be $50\mathrm{m}$ apart. Using his stopwatch, Desmond notices that it takes $3\mathrm{s}$ for most cars to travel from the one pole to the other.
   1. Using the equation for velocity ( $v$ = $\frac{\Delta x}{\Delta t}$ ), show all the working needed to calculate the velocity of a car travelling from the left to the right.
   2. If Desmond measures the velocity of a red Golf to be $-\mathrm{16,67}\mathrm{m}·\mathrm{s}{}^{-1}$ , in which direction was the Gold travelling? Desmond leaves his stopwatch running, and notices that at $t=\mathrm{5,0}\mathrm{s}$ , a taxi passes the left pole at the same time as a bus passes the right pole. At time $t=\mathrm{7,5}\mathrm{s}$ the taxi passes the right pole. At time $t=\mathrm{9,0}\mathrm{s}$ , the bus passes the left pole.
   3. How long did it take the taxi and the bus to travel the distance between the poles? (Calculate the time interval ( $\Delta t$ ) for both the taxi and the bus).
   4. What was the velocity of the taxi and the bus?
   5. What was the speed of the taxi and the bus?
   6. What was the speed of taxi and the bus in $\mathrm{km}·\mathrm{h}{}^{-1}$ ?

   

3. A rabbit runs across a freeway. There is a car, $100\mathrm{m}$ away travelling towards the rabbit.

   

   1. If the car is travelling at $120\mathrm{km}·\mathrm{h}{}^{-1}$ , what is the car's speed in $\mathrm{m}·\mathrm{s}{}^{-1}$ .
   2. How long will it take the a car to travel $100\mathrm{m}$ ?
   3. If the rabbit is running at $10\mathrm{km}·\mathrm{h}{}^{-1}$ , what is its speed in $\mathrm{m}·\mathrm{s}{}^{-1}$ ?
   4. If the freeway has 3 lanes, and each lane is $3\mathrm{m}$ wide, how long will it take for the rabbit to cross all three lanes?
   5. If the car is travelling in the furthermost lane from the rabbit, will the rabbit be able to cross all 3 lanes of the freeway safely?

Investigation : an exercise in safety

Divide into groups of 4 and perform the following investigation. Each group will be performing the same investigation, but the aim for each group will be different.

1. Choose an aim for your investigation from the following list and formulate a hypothesis:
   • Do cars travel at the correct speed limit?
   • Is is safe to cross the road outside of a pedestrian crossing?
   • Does the colour of your car determine the speed you are travelling at?
   • Any other relevant question that you would like to investigate.
2. On a road that you often cross, measure out $50\mathrm{m}$ along a straight section, far away from traffic lights or intersections.
3. Use a stopwatch to record the time each of 20 cars take to travel the $50\mathrm{m}$ section you measured.
4. Design a table to represent your results. Use the results to answer the question posed in the aim of the investigation. You might need to do some more measurements for your investigation. Plan in your group what else needs to be done.
5. Complete any additional measurements and write up your investigation under the following headings:
   • Aim and Hypothesis
   • Apparatus
   • Method
   • Results
   • Discussion
   • Conclusion
6. Answer the following questions:
   1. How many cars took less than $3\mathrm{s}$ to travel $50\mathrm{m}$ ?
   2. What was the shortest time a car took to travel $50\mathrm{m}$ ?
   3. What was the average time taken by the 20 cars?
   4. What was the average speed of the 20 cars?
   5. Convert the average speed to $\mathrm{km}·\mathrm{h}{}^{-1}$ .