A car moves from rest with a constant acceleration of 4m/s squared for 5s .IT then continues with the speed attained for10s and then accelerates at 2m/s squared for 10s.A/ SKETCH A SPEED TIME GRAPH FOR THE WHOLE MOTION GIVING YOUR VALUES ON BOTH AXES.B/CALCULATE THE AVERAGE SPEED OF THE CAR DURING THE MOTION.
graph it. At the end of each time period, the beginning speed is what the previous graph segment ended at.
average speed is a little more difficult.
Average speed is not (Vf+Vi)/2, as some will try to tell you.
What average speed is total distance/time
So you need total distance.
so figure distance this way. On your graph, make a grid of squares below the curves/lines. Now distance is speed*time, so figure immediately what your square scale is in speed, and time. Now count the squares, and estimate the area, that is then distance traveled.
see this as an example (IT IS NOT YOUR PROBLEM). The area below the graph is distance. http://docs.engineeringtoolbox.com/documents/1373/speed-time-graph.png
A) To sketch a speed-time graph for the given motion, we need to break the motion into different intervals and calculate the speed during each interval.
Interval 1: The car moves from rest with a constant acceleration of 4 m/s² for 5 s. During this interval, we can use the equation for uniformly accelerated motion:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
Since the car starts from rest (u = 0 m/s), the equation simplifies to:
v = at
v = 4 m/s² * 5 s = 20 m/s
During this interval, the speed increases linearly from 0 m/s to 20 m/s.
Interval 2: The car continues with the speed attained for 10 s. Since the speed remains constant, the speed-time graph will be a horizontal line at 20 m/s for this interval.
Interval 3: The car accelerates at 2 m/s² for 10 s. Again, using the equation for uniformly accelerated motion:
v = u + at
Since the initial velocity is 20 m/s (from interval 2), and the acceleration is 2 m/s², the equation becomes:
v = 20 m/s + 2 m/s² * 10 s = 40 m/s
During this interval, the speed increases linearly from 20 m/s to 40 m/s.
Putting all the intervals together, the speed-time graph would look like this:
|
|
40 -------------- ____
| \
20 -------------- \
| \
0 ------|--------------|--------------|--
0 5 15 25
Time (s)
B) To calculate the average speed of the car during the motion, we need to find the total distance traveled and divide it by the total time taken.
Distance during interval 1 = 0.5 * (u + v) * t
= 0.5 * (0 + 20) * 5
= 50 m
Distance during interval 2 = v * t
= 20 m/s * 10 s
= 200 m
Distance during interval 3 = 0.5 * (u + v) * t
= 0.5 * (20 + 40) * 10
= 300 m
Total distance traveled = Distance interval 1 + Distance interval 2 + Distance interval 3
= 50 m + 200 m + 300 m
= 550 m
Total time taken = Time interval 1 + Time interval 2 + Time interval 3
= 5 s + 10 s + 10 s
= 25 s
Average speed = Total distance / Total time
= 550 m / 25 s
= 22 m/s
Therefore, the average speed of the car during the motion is 22 m/s.