# Resultant force when a body is accelerating

1. Jun 8, 2014

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

There is a body of mass 500kg accelerating at 2.5ms^-2.
It experiences a frictional force of 1000N.

2. Relevant equations

Resultant Force = ma

3. The attempt at a solution

Resultant Force = (500)(2.5)N = 1250N
The body is moving forward with a net force of 1250N
A frictional force of 1000N is acting on the opposite direction.
The body must be moving with this forward force:

Forward Force - Frictional Force = Resultant Force
Forward Force = (1250 + 1000)N = 2250N

But what does all this mean?

The body is accelerating. Shouldn't the forward force as well as the frictional force be continuously increasing?

2. Jun 8, 2014

### Staff: Mentor

If the acceleration is constant, the net force must be constant. No reason to think that the frictional force is changing.

What an acceleration means is that the velocity is continuously changing, not the force.

3. Jun 8, 2014

### BruceW

yeah, in most real-world situations the friction force will increase in this scenario. But the question specifically states that the friction force is constant. So as always, you should do as the question says.

4. Jun 8, 2014

Here is the scenario:

At t=0s,
The body has a forward force of 2250N and a frictional force of 1000N
F res = 1250N

At t=1s or any time in the future,
The body will still have a forward force of 2250N and a frictional force of 1000N
F res = 1250N

Will it have a constant velocity or acceleration? How?

From what you said, if there is constant acceleration, there will be a resultant force. If there is constant speed, there would be no resultant force? How? Is there any equation?

5. Jun 8, 2014

$\vec{F}=m\vec{a}$
If there is a constant speed, acceleration is zero,therefore net force is zero

6. Jun 8, 2014

The same equation :$F=ma$. If the force and mass is constant, acceleration is constant and speed is changing(As acceleration is defined as the change of speed with respect to time. $\frac{dv}{dt}$

7. Jun 8, 2014

### Staff: Mentor

Right. (Unless you are told otherwise, assume the givens stay the same.)

As long as the forces do not change, neither will the acceleration.

The equation is simply Newton's 2nd law:
∑F = ma

When the velocity is constant the acceleration will be zero. Thus the net force will be zero.

8. Jun 8, 2014