# F = m x a, but what if velocity is constant (making a zero)?

1. Jul 2, 2010

### lrl4565

So, Force = Mass x Acceleration. Alright, but what happens when a 400 pound truck hits you going at a constant velocity of 70 miles per hour? Acceleration is 0. Does this mean that the truck exerts no force?

2. Jul 2, 2010

### rcgldr

You're acceleration wouldn't be zero, you'd accelerate from 0 to 70 mph or more depending on how elastic you are (how fast you bounce off). The truck would slow down quite a bit if it only weighed 400lbs.

3. Jul 2, 2010

### n.karthick

Certainly it will exert a force, but momentum will be conserved.

4. Jul 2, 2010

### hikaru1221

No. When you are still in contact with the truck, the truck does exert force on you, which is why you gain speed from zero when being hit. The time period of the contact is typically very small, which I think leads to your misconception that the truck exerts no force. Only after you lose the contact, it no longer exerts any force, and you will travel to the hospital at the constant speed 70 miles/hour if there is no friction or nothing on your way.

5. Jul 2, 2010

### phyzmatix

You've received three replies, I know, but let's put it all together. Let's refer back to Newton's Laws of Motion

In this case, the truck is subject to Newton's first Law

You, however, will be subject to the second

You will experience an impulse as the impact with the truck accelerates your body from its stationary state, so (as previously mentioned) the truck's acceleration is zero i.e. there are no forces (ideal world) exerted on the truck whereas your acceleration will be >0 i.e. there will be a force exerted on you by the truck (and on the truck by you, 3rd law).

Makes sense?

6. Jul 2, 2010

### inky

I think before collision speed of truck is constant but after collision speed is not constant. So it has acceleration. Now we can consider force.

7. Jul 2, 2010

### Staff: Mentor

Force = mass X acceleration refers to the net force on an object. As long as the truck moves at a constant velocity, the net force on the truck will be zero. Of course, as soon as the truck hits you, it will no longer be moving at a constant velocity--there will be a non-zero acceleration. You and the truck will definitely exert forces on each other.

8. Jul 2, 2010

### arildno

In order to find out the (average) magnitude of the force couple you and the car exert upon each other during the colllision, you'll need to know the a) mass of at least one of the objects, b) the velocities of that object just before, and just after the collision, and c) the time the collision took.

Let us define these cquantities as:
$$m, v_{before},v_{after},T$$

Thus, the force upon the object during the collision is roughly given by:
$$F=m\frac{v_{after}-v_{before}}{T}$$
Note that for even a "tiny" velocity difference, the force might be enormous, if the time interval over which the velocity change happened was even tinier.

9. Jul 2, 2010

### pahr samsalah

The answer is in your question .Since the truck is deaccelerating from 70mileshr-1 to 0mileshr-1 .Since this change is taking place in time 't' so a=70/t.
Practically this time will be very small (i.e in the order of 1*10^-1) so this force must be very large (i.e a=70/10^-4=7x10^-5 , assuming t=10^-4).But since it acts only for a short time therefore change in momemtum is small and not very large.

10. Jul 2, 2010

### Ali Inam

Obviously, there will be force when the truck is about to hit us while coming with a great speed but as you say the acceleration will be zero, so it will face retardation at the point of impact on you and naturally hit you with a THUMP !!

We supposed this example after removing friction, didn't we ? !

11. Jul 2, 2010

### Fredrik

Staff Emeritus
The acceleration isn't going to be zero when the truck makes contact with you. Anyway, the acceleration of the truck is only relevant when you want to know the force that you exert on the truck. If you want to know the force that the truck exerts on you, it's your acceleration that matters, and I can assure you that it will be substantial.