Knowledge and Understanding of Kinematics

## Question:

Hi having another problem,

If a car is travelling with a constant acceleration covers a distance between to points 60 m apart in 6.0 s . It's speed as it passes the second point is 15ms,

a) what is it's speed at the first point

b) what is it's acceleration

c) at what prior distance from the fisrt point was the car at rest
I am having difficulty trying to choose which equation of kinematics to use on these 3 questions.

Could you please guide me in the right direction

Thank you very much

## Answer:

First a brief observation on the difference between knowledge and understanding. It is possible to learn the equations presented in kinematics, making them part of your knowledge. There are questions that may test that knowledge by setting forth problems that simply require the application of one of these equations to get the solution. The questions you have been having trouble with deal not so much with knowledge but with understanding. If you really understand what constant acceleration implies you can solve these more sophisticated problems, even if you do not know the kinematics equations.
Constant acceleration means that the average speed may be calculated in a simple way from the initial speed and the final speed. It is just the arithmetic average (vi+vf)/2. Another expression for average speed is the distance covered divided by the time it took. Average speed is average speed no matter how it is calculated so (vi+vf)/2=60/6=10m/s. But we are given the fact that vf=15m/s so vi must be 5m/s to make (vi+vf)/2=10.

The acceleration, being constant, is simply calculated by the change in speed divided by the time it took, or (15-5)/2m/s/s = 5m/s/s.

With constant acceleration of 5 m/s/s it will take 1 second to reach the initial speed and therefore the initial point. The average speed between rest and the initial point is (0+5)/2m/s = 2.5m/s. At an average speed of 2.5m/s, in 1 second the distance covered is 2.5 meters.

Again, if my arithmetic is correct, we have arrived at the solution without plugging any of the kinematics equations directly. Understanding is a much more powerful tool than is knowledge. It allows you to answer questions that have never been previously asked. People pay good money to anyone with that ability.