A car has a velocity of 25 metres per second as it passes a road sign. At that point, the car’s wheels push the car forward with a force of 550 newtons. And the friction between the car’s wheels and the road applies a force of 550 newtons in the opposite direction to the car’s motion. What is the velocity of the car 10 seconds after it passes the sign? Assume no other forces act in this time.
Okay, so, in this question what we have is a car moving along a road. And we’ve been told that this car passes a road sign. Now at the point that the car passes the road sign, we’ve been told that the car’s wheels push the car forward with a force of 550 newtons. So, what we can do is to draw a force in the forward direction on the car. And we can label that force 550 newtons.
Now as well as this, we’ve been told that the friction between the car’s wheels and the road applies a 550-newton force in the opposite direction to the car’s motion. But then, we know that the car is moving towards the right, as we’ve drawn it, moving past the road sign. And so, in the orientation that we’ve drawn the diagram, we can say that the friction force acts in this direction. And that force is also 550 newtons.
Now as well as this, we’ve been told to assume that no other forces are acting on the car when it passes the sign. And therefore, the two forces that we’ve already drawn, the 550-newton force forward and 550-newton force backward, are the only forces acting on the car. But then, in this situation, because the two forces are acting in opposite directions, they work to cancel each other out. And because their magnitudes are exactly the same, they cancel each other out perfectly.
In other words, we can say that the net force on the car, which is basically a fancy way of saying what the overall resultant force on the car will be, is going to be zero newtons. Because the situation where there are two forces acting on the car, each with the same magnitude and acting in opposite directions, is identical to the situation in which the car would have no forces acting on it at all. And another way to say this is that the overall, or net force, on the car is zero newtons.
The reason this is important is because we can then recall Newton’s first law of motion. Newton’s first law of motion tells us that an object at rest remains at rest and an object moving with a constant velocity continues to travel with that same constant velocity unless it is acted on by an unbalanced force.
Now the reason that this is relevant to our car is because we’ve already seen that the net force on the car is zero newtons. In other words, the forward 550-newton force is exactly balanced by the backward 550-newton force. And therefore, there is no unbalanced force on the car.
But then this means that the car, which was initially travelling with a velocity of 25 metres per second, will continue to travel with that same constant velocity. Now, of course, velocity is a vector quantity. So, we need to think about the speed and the direction of the car. However, importantly, we weren’t given information about the direction in which the car is travelling in the question itself. We just arbitrarily chose to draw a diagram so that the car was moving towards the right. And so, if we weren’t given this information in the question, then we can’t give it in our answer either.
So, when we’re asked to find the velocity of the car 10 seconds after it passes the sign, then we know that the car must be moving at 25 metres per second still. Because, as we said, there is no net force acting on the car. So, there is no unbalanced force on the car. However, we can’t say anything about the direction which the car is travelling.
And so, we can say that our final answer is that the velocity of the car 10 seconds after it passes the sign is 25 metres per second. And this constant velocity of the car would still be the same however many seconds or minutes or hours after the car passed the sign, assuming that the forces on the car didn’t change in any way.
And so, the fact that we’ve been given a specific time value after which to calculate the speed of the car is a bit of a red herring. And so, all we can say with certainty is that the velocity of the car is 25 metres per second.