1. Acceleration & Distance Uniform Acceleration, Starting from rest
Notes on Motion V
Acceleration & Distance
Uniform Acceleration, Starting from rest

2. When you graphed your data, it should have looked something like this.
Your Acceleration Lab
In your lab you allowed your cart to accelerate uniformly from rest and compared the distance it travelled with time.
When you graphed your data, it should have looked something like this.

3. Your Acceleration Lab
You were also asked to do a motion diagram for your cart.
First you probably drew a scale.
Then you plotted distances at equal time intervals on your scale.
You now have a motion diagram for your accelerated cart!!!!
0 cm
20 cm
40 cm
60 cm
80 cm
100 cm

4. Your graph and your motion diagram showed the same relationship between distance and time. Both showed that as your time increased the distance traveled by your cart in equal time intervals increased.
0 cm
20 cm
40 cm
60 cm
80 cm
100 cm
4 cm
12 cm
20 cm
28 cm
36 cm
Time Interval
Total Distance Travelled from Start (cm)
Distance Travelled during Time Interval (cm)
0 to 2 4
2 to 4 16
4 to 6 36
6 to 8 64
8 to 10
100

5. Why does this happen?
0 cm
20 cm
40 cm
60 cm
80 cm
100 cm
Time Interval
Total Distance Travelled from Start (cm)
Distance Travelled during Time Interval (cm)
0 to 2 4
2 to 4 16 12
4 to 6 36 20
6 to 8 64 28
8 to 10
100
Since the direction of motion and the uniform acceleration of your cart are in the same direction the cart is speeding up. So for each time interval the cart is going faster and covering more distance since the time intervals are equal.

6. The shape of your graph of distance vs time is a parabola.
Now We NEED a Formula that Relates Distance (d), Uniform Acceleration (a) and Time (t)
In your experiment, your cart started from rest and had a uniform acceleration. For our purposes, all of our uniformly accelerated objects will also start from rest.
The shape of your graph of distance vs time is a parabola.
Since parabolas have equations that look like y=x2, our formula for distance should involve d and t2.

7. In our data, the distance is the square of the time!!!!
Now We NEED a Formula that Relates Distance (d), Uniform Acceleration (a) and Time (t)
In your experiment, your cart started from rest and had a uniform acceleration. For our purposes, all of our uniformly accelerated objects will also start from rest.
Time
Total Distance Travelled from Start (cm) 2 4 16 6 36 8 64 10
100
Do you notice anything about the distance data when compared to the time data for your cart? 02 22
In our data, the distance is the square of the time!!!! 42
So our table also shows that our formula relating distance and time for our accelerating cart should involve d and t2 62 82
102

8. Now We NEED a Formula that Relates Distance (d), Uniform Acceleration (a) and Time (t)
In your experiment, your cart started from rest and had a uniform acceleration. For our purposes, all of our uniformly accelerated objects will also start from rest.
It turns out that the formula we will use to describe the relationship between distance (d), uniform acceleration (a) and time (t) is:
JUST TRUST ME

9. Now We NEED a Formula that Relates Distance (d), Uniform Acceleration (a) and Time (t)
If we solve this equation for the acceleration (a), we have a formula for finding the acceleration of an object that travels a distance, d, in a time, t.
Remember, this only is used if the object starts from rest and has a uniform acceleration!!!!!!!!!

10. Now We NEED a Formula that Relates Distance (d), Uniform Acceleration (a) and Time (t)
If we solve this equation for the time (t), we have a formula for finding the time an object travels with acceleration (a) for a distance (d).
Remember, this only is used if the object starts from rest and has a uniform acceleration!!!!!!!!!

11. Example Problem 1
Find the distance travelled by a car that accelerates uniformly from rest at 3.0-m/s2 for 25-s.
Know
Find
Useful Formulas
a = 3.0-m/s2
t = 25-s
d = ?
Solution
Formula

12. Example Problem 2
A car starts from rest and accelerates uniformly at 0.25-m/s2. How long will it take to cover 50-m?
Know
Find
Useful Formulas
a = 0.25-m/s2
d = 50-m
t = ?
Formula
Solution

13. Example Problem 3
What uniform acceleration would a football player need to have to cover 100-m in 12-s?
Know
Find
Useful Formulas
d = 100-m
t = 12-s
a = ?
Formula
Solution