A 1370-kg car is skidding to a stop along a horizontal surface. The car decelerates from 27.6 m/s to a rest position in 3.15 seconds. Assuming negligible air resistance, determine the coefficient of friction between the car tires and the road surface.
source: https://www.physicsclassroom.com/calcpad/newtlaws/prob30.cfm
I have got this question here but i am a bit stuck when i got force friction is equal to force applied which is $F=ma$. Acceleration appears to be negative and as a result, the force applied is a negative value. What does this mean? I know that negative involves direction but i still do not fully understand how to use the negative sign. So do we always assume the object is going to the right or in x-axis? If that so, f=negative doesn't make sense. Does that also mean that the friction is positive and going right?
Best Answer
Positive and negative depends on your chosen coordinate system. When you choose a direction to be "positive", you're choosing a coordinate system. Acceleration is the time derivative of velocity and is a vector. In a one-dimensional problem, its direction is uniquely determined by its sign (there are only 2 possible directions; positive and negative). It may look like a scalar in this case, but it really is a vector. When acceleration is positive, it tells us that the velocity is moving to the right on the number line.
Negative acceleration, on the other hand, means that the object's velocity is decreasing (either slowing down in the positive direction or speeding up in the negative direction) i.e. moving to the left on the number line. It does not tell us how close to zero on the number line the velocity is. That is the job of the term "speed", which tells us the magnitude of the velocity, how far it is from zero. Both positive and negative acceleration can cause an object to speed up (in the respective directions). An object moving to the left and speeding up will have a very different motion compared to an object moving to the right and slowing down, yet both have would negative acceleration as their velocities are both moving to the left on the number line. Be careful when distinguishing "decreasing velocity" with "slowing down"; the former talks about velocity, while the latter talks about the speed.
In summary, acceleration itself tells us nothing about the velocity at which the object is already traveling at, it only tells us how fast and in which direction its velocity is changing. Hence the constant term when acceleration is integrated with respect to time.