# Distance traveled with acceleration & deceleration

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1. Aug 5, 2015

### mattcom1

1. The problem statement, all variables and given/known data
A man bungee jumps off a cliff and free falls for 3 seconds. The bungee cord stops the jumper in 5 seconds. How far did the man fall in total?

2. Relevant equations
X = V0t + 1/2at2

3. The attempt at a solution
Xf = X1 + X2

X1 = V1it1 + 1/2a1t12
X1 = 0 * 3 + 1/2 * -9.8 * 32
X1 = -44.1m or 44.1m (not sure if I should keep this absolute value or not...)

X2 = V2it2 + 1/2a2t22
v2i = v1f = a1 * t1
a2 = Δv/t = (v2f - v2i)/t = (v2f - (a1*t1))/t2
a2 = (0 - (-9.8*3))/5 = 5.88
X2 = (-9.8 * 3) * 5 + 1/2 * 5.88 * 25
X2 = either -73.5m, 73.5m, or 220.5m [(9.8*3)*5 + 1/2*5.88*25] ? depending on whether everything is in absolute values or not, once again, I'm not sure.

Xf = -44.1m + -73.5m
Xf = -117.6m or 117.6m

Thanks!

2. Aug 5, 2015

### Qwertywerty

Is acceleration due to gravity +ve or -ve ?

Your method is basically correct . What you need to do is understand your sign convention .

Hope this helps .

3. Aug 5, 2015

### PeroK

If you want a quick way to solve problems like this, think about the average speed for each part of the fall. I assume the bungee deceleration is taken to be constant?

4. Aug 5, 2015

### mattcom1

I'm glad to hear I'm not too far off on the methodology. I'm going to stick with -ve for gravity.

Yes, I believe that the deceleration is intended to be constant.

5. Aug 5, 2015

### PeroK

Try to find the quick way! First, what's the average speed for the free fall?

6. Aug 5, 2015

### mattcom1

Hmmm... The only formula I know for average velocity is: Avg Velocity = Distance/Time. Distance is unknown and Avg Velocity is unknown. Is there another equation for avg velocity that I'm not aware of?

7. Aug 5, 2015

### PeroK

For constant acceleration from rest, average velocity is $\frac{at}{2}$

8. Aug 5, 2015

### mattcom1

Interesting. Let me give it a go.

X = V1avg * t1 + V2avg * t2
X = 0.5 * a1t1 * t1 + 0.5 * a2t2 * t2
X = (0.5 * -9.8 * 3) * 3+ (0.5 * 5.88 * 5) * 5
X = -44.1 + 73.5

similar numbers as the first way, but a different sign... Certainly something else to consider! Thanks!

9. Aug 5, 2015

### PeroK

You need to be careful with your signs. IMHO, you are trying to plug numbers into equations without thinking enough. If gravity is negative, then the downward direction is negative, so all your displacements and velocities should be negative.

In this case, it would have been better, therefore, to take the downward direction as positive.

Here's another question: what can you say about the average velocity for the free fall and the deceleration?

10. Aug 5, 2015

### Qwertywerty

You seem to be confused with your acceleration .
If this is the case , first assign your convention .

For example , let upward direction be -ve and downward +ve . Now , solve everything following this convention - Remember , all your variables ( except t ) are vectors , so pay careful attention to the sign .