Can someone help me with these graph?

Question

t (s): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
x (s): 0, 5, 20, 45, 80, 90, 100, 100, 100, 100, 80, 60

1. find the greatest speed. I don't know which one it is since there are 4 points of "100"
2. least speed? Do I count "0" or"1"?
3. the speed is constant? would I choose 6, 7, 8,9?
4. average speed of particles for the first 7 s?
5. find the instantaneous speed of the particles at 3s.

Could someone explain all of this to me?

Answer 1

Plot 't' along x-axis and 'x' along y-axis i.e. you have to draw a 'x' vs 't' graph. The points will have coordinates: (0,0), (1,5), (2,20), (3,45), ....... etc.

It appears to me that 'x' is speed and 't' is time. As speed is constant for the time 6 to 9 seconds so it is clear that speed is maximum for any point in this time span.

Least speed = 0

speed constant: t = 6 to t = 9

avg. speed = (0 + 5 + 20 + 45 + 80 + 90 + 100)/7

instantaneous speed = 20

Answer 2

If i'm not wrong, x represents the particle position, and not the speed. So..

1. To find the greatest speed would be to find the instance in time where the particle changes its position the most. We see that between the 3rd and 4th second, the position changes by 35. So the greatest speed is 35units/second

2. The least speed is 0, as apparent from the time from 6s to 9s, where the particle is at the same position.

3. Speed is constant from 4-6s, from 6-9s, and from 9-11s

4. The average speed would be the distance travelled in 7 sec divided by the time. Therefore, 100/7 = 14.3units/second

5. The instantaneous speed at 3 sec would be (45-20)/(3-2) = 25units/second

Hopefully i'm correct.

Answer 3

S speed =distance/time
1. Greatest speed= biggest distance/second
In this instance it is80-45=35 units per second.
2. Least speed =least distance per second= 100-100units /one second( between 7and 8 seconds)= 0 units per sec
3. The distance does not change for all the 100s so the speed is constantly zero.Also between the last 100 and the next 80 the speed is 20 units/second as it is between 80 and 60.
4.Average speed =distance/time=100 units/7seconds=14.3units per second.
5.There is not enough information to give a precise value for the speed at 3 seconds.
you could make a graph of the values and estimate the slope at 3 seconds.An approximation is to average the average speed at 4 seconds and at 2 seconds.
speed at 4 seconds =80-45 per sec=35/sec
speed at 2seconds =45-20 per sec =15/sec
estimated speed at 3 secs =25 units/sec
you should not take an average of average in normal circumstances.

Answer 4

Here is a start:

to find the speeds, you need to look at the rate of change of x against t. for example between t=2 and t=3, we have,

(change in x) / (change in t) = (45 - 20) / (3 - 2) = 25

its easiest to find these by graphing x against t

the least speed it when

(change in x) / (change in t) is closest to zero. in this case, the vale of x (distance) does not change between certain times, so at these times, the speed will be zero. since change in x is zero and therefore above equation = 0

speed is constant when

(change in x) / (change in t) = (change in x) / (change in t) for different times. an example would be when t=6 to t=9 since the speed is constant at 0.

try the rest yourself

Answer 5

100
0
6,7,8,9
62.85
25