Hi, I need some help with a homework problem invovling acceleration

AI Thread Summary
To find the acceleration of the car, the change in velocity over time is calculated using the formula a = Δv/t. The velocity changes from 8.8 m/s to 53.25 m/s over a period of 20 seconds, resulting in an acceleration of approximately 2.2225 m/s². The discussion also highlights the importance of the trendline equation v(t) = 3.6688t + 5.6189, which represents the slope of the velocity graph. This slope, or gradient, is another way to determine acceleration. Understanding both the calculation and the trendline is essential for completing the homework problem accurately.
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Homework Statement


What is the acceleration of your car?

Time Velocity[ms]
1 8.8
2 12.82
3 16.25
4 20.46
5 24.22
6 28.09
7 31.77
8 35.24
9 39.32
10 42.37
11 44.61
12 46.63
13 49.01
14 50.53
15 52.1
16 52.32
17 53.6
18 53.44
19 53.74
20 53.25

http://img87.imageshack.us/img87/8674/velocitygraphob6.jpg


Homework Equations





The Attempt at a Solution

 
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I really just don't know where to start, is there an equation I need to use or is this much more complicated?
 
The definition of acceleration is the rate of change of velocity with time. What you need to do is find out how much the speed changed and in what time, then:

a= \frac{\Delta v}{t}
 
(53.25 - 8.8) = 44.45

a = (44.45) / 20s

a = 2.2225 m/s

Is this right?
 
What's with the function in the upper right edge v(t) = 3.6688 t + 5.6189 ?
 
That's just the slope of the trendline for the increasing part of the graph. He told us in class we had to show it.
 
Ok, so from above a= \frac{\Delta v}{t} , or to put it another way, a is the gradient of the graph of v against t. Given your trendline, in the form y=mx+c, how can you read off the gradient?
 

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