chapter "1" , Lesson # 2.a

1.2 Motion study

Let's follow Mr Samer's car one morning and trace his journey as he drives his son Bara' to his school.

Bara' checks his digital Watch which registers 06:10 a.m. when Mr Samer starts his car engine. Let's Call this time t = 0 s,  Bara' watches the speedometer carfully at each minute interval.

Distance-time graph 

we can translate the information gathered by Bara' into a table of distance travelled (d), by the car against time (t), and Plot distance-time graph, as shown below

The distance-time graph of the journey 

As observed from the distance-time graph, Mr Samer does not drive at a constant or uniform speed. In the first minute, from t= 0 min to t=1 min, the distance covered by the car is 0.20 km, which gives the average speed of the car as 0.020 km/ min. The distance covered during the second minute is 0.30 km, giving the average speed during the second minute as 0.30 km/ min.

  

Average speed( t=0 min to t =1min = 0) = 0.20 /1 = 0.20 km/h

Average speed( t=1 min to t =1min = 2) = 0.30 /1 = 0.30 km/h

It Can be observed from the distance-time graph that the slope of the curve between t = 0 min to t = 2 min increases and it represent the " instantaneous speed" during this period. Hence the car's speed is increasing. We say that the car is accelerating. 

However, during the next four minutes, from t = 2 min to t= 6 min, the distance covered by the car is uniform or constant at 0.50 km for every one minute. Hence the car travels at a uniform speed of 0.50 km/min during this period;

Slope(t =2-3min) = (1-0.5)/(3-2) = 0.5 /1 = 0.5 km/min (average speed)

Slope(t =5-6min) = (2.5-2)/(6-5) = 0.5 /1 = 0.5 km/min (average speed)

The uniform speed from t = 2 min to t=6 min is demonstrated by a straight line with uniform slope "gradient".

Uniform speed (t=2 min to t= 6 min) = slope "gradient" (t=2 min to t= 6 min)
                                                        = 2.5 - 0.5  =  0.2    = 0.5 km /min

                                                                6-2           4

During the next 3 minutes from t = 6 min.to t = 9 min. the Car slows down as the distance covered by the car each minute later decreases is from 0.3 km to 0.05 km, the speed of the car decreases from 0.3 km /min to 0.05 km/ min, The slope "gradient" of the distance - time graph shows corresponding decrease.

During the last one minute of its journey the car is at rest as the distance traveled is zero. the slope "gradient" of distance - time graph is zero.

Graphical summary of the motion:

*** Test yourself "on Facebook"

Sketch the distance- time graph of a body that is travelling 
(a) at constant speed,
(b) with increasing speed; and
(c) with decreasing speed