# Acceleration problem and distance

1. Oct 1, 2009

### 1irishman

1. The problem statement, all variables and given/known data
Fred and Wilma leave their house at the same time heading for the bus stop 100m away. Fred starts at rest, accelerates at 0.500 m/s^2 up to a maximum speed of 5.00m/s, which he holds as he runs for the bus stop. Wilma gives Fred a 5.00 second head start and then accelerates for 6.00 seconds up to her maximum speed of 6.00m/s. Who gets to the bus stop first, and how long do they wait for the second person to arrive?

2. Relevant equations
v=d/t
d=vit + 1/2 at^2
vf=vi+at

3. The attempt at a solution
i have Fred accelerates for 10 seconds. and in 10 seconds he covered a distance of 25m. plus his acceleration distance of 6.25m = 31.25m total. 100m minus 31.25m is 68.75m remaining distance at constant speed so t=d/v so 68.75/5 = 13.75 s plus 11 seconds is 24.75. The answer in the book for Fred's time says 25seconds and the answer in the book for Wilma says 24.7seconds. Am i right here? It feels like i'm getting closer to the answer unless i've already got it?

2. Oct 1, 2009

### Andrew Mason

Why are you adding 6.25 m? You have already determined his acceleration distance is 25m.

The answer in the book is right.

AM

3. Oct 1, 2009

### 1irishman

Fred's acceleration distance is 25metres. So i got 100m-25m=75m left for Fred plugged into t=d/v=75/5=15 seconds plus 11seconds equals 26seconds. Why am i one second off the correct answer of 25seconds? Please help? thanks.

4. Oct 1, 2009

### Andrew Mason

How do you get 11 seconds? What is $\Delta t$ in terms of $\Delta v$ and a?

AM

5. Oct 2, 2009

### 1irishman

I can't solve this...please give me more hints?

6. Oct 2, 2009

### Andrew Mason

Explain how you get 11 seconds.

If $a = \Delta v /\Delta t$ and a = .5 m/s^2, vf = 5 m/s and vi = 0 you should be able to work out the time. It is not 11 seconds.

AM

7. Oct 2, 2009

### 1irishman

okay...i have t=10s for Fred to accelerate, and 15s at constant speed for Fred total time is 25seconds. Is that right for Fred?
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For Wilma I have 13.7s at constant speed plus 11seconds to include acceleration time is 24.7seconds. Is that right for Wilma?

8. Oct 2, 2009

AM