# Elementary - braking force of a trolley

1. Oct 19, 2012

### Glyper

1. The problem statement, all variables and given/known data

A trolley weighing 16 000kg is moving along a horizontal surface with a velocity od 6m/s. What braking force would cause it to brake on a distance of 10m and how long it would take?

2. Relevant equations

a = F/m = ΔV/t

3. The attempt at a solution

So ΔV = 6m/s, m=16 000kg, s = 10m and F = mΔV/Δt. We know neither F nor t so how could I solve this? It's just one equation but two unknown variables. Could you please help?

2. Oct 19, 2012

### Basic_Physics

Do you know the relationships between the work done by a force acting on a body and its energy?

3. Oct 19, 2012

### Glyper

I know Newton's laws of motion, that's why I have the a=F/m, but what does that give me?

4. Oct 19, 2012

### HallsofIvy

Staff Emeritus
If a, acceleration, is constant, then v= at+ v0 and d= (1/2)at^2+ v0t.

You know that v0= 6 m/s and that d= 10m . Solve the quadratic equation (1/2)at^2+ 6t- 10= 0 for t, with parameter a. The final velocity was 0 so at+ 6= 0. Put the result you got for t into that and solve the resulting equation for a.

5. Oct 19, 2012

### Basic_Physics

Rather have a look at the chapter on work and energy.

6. Oct 19, 2012

### lep11

Do you know what the answer should be?

7. Oct 20, 2012

### Glyper

HallsofIvy - OK, thank you. So we get t = (2 (sqrt(5 a+9)-3))/a (the other one is negative so doesn't matter), we plug it into the latter and get (2 (sqrt(5 a+9)-3) so (sqrt(5 a+9)=3 but then... a would have to be 0, which it's not, is it? Where did I make a mistake?

8. Oct 20, 2012

### Glyper

Could someone please tell me where did I make a mistake? :(

9. Oct 21, 2012

### Glyper

No matter what I do to the expression, it never outputs anything other than 0 - why? Do I lack some variable?