Find what is wrong with the statement based on knowledge of a derivative and its meaning.

Question

if the position of the car at time t is given by s(t) then the velocity of the car is s'(t) and the units of s' are meters per second.

 

I have to find what is wrong with this statement but all of the parts look accurate. I can't seem to find what is wrong. please help me figure this out.

Thanks in advance!

 

Answer 1

The statement as written is not really wrong, but is incomplete with respect to units of measurement.    

 

 The statement would be clearer if rewritten in a way such as:

 

If the position of the car at time t seconds is given by s(t), where s(t) is measured in meters, then the velocity of the car at time t seconds is s'(t), where s'(t) is measured in meters/second.  

Answer 2

Posiition = s(t)                 [units of meters]
Velocity = s’(t)               [units of meters/sec]
Acceleration = s’’(t)         [units of meters/sec²]

 

Usually, s would better indicate speed than position, but it is o.k.  Also, speed is a scalar and velocity is a vector (direction-aware).

 

In the problem statement, the units of position must be meters and the units of time must be seconds in order to have the units of velocity be meters/sec [this omission is poor].