Correct question is;
Consider these statements written in ordinary language:
A The speed of the car is proportional to the distance it has traveled.
B The car is speeding up.
C The car is slowing down.
D The car always travels the same distance in the same time interval.
E We are driving backwards.
F Our acceleration is decreasing. Denoting by s(t) the distance covered by the car at time t, and letting k denote a constant, match these statements with the following mathematical statements by entering the letters A through F on the appropriate boxes:
s′′<0.
s′ is constant
s′<0
s′′′<0
s′′>0
s′=ks
Answer:
Answers given below.
Step-by-step explanation:
F) acceleration is the second derivative of distance with respect to time.
Thus; s'' < 0
D) Car travels the same distance in the same time interval. This means the speed is constant. Speed is the first derivative of distance with time. Thus;
s' is constant
E) Driving backwards means that speed is; s' < 0
C) Car is slowing down means negative acceleration. Thus; s'' < 0
B) Car is speeding up means acceleration is greater than 0. Thus: s'' > 0
A) Car speed being proportional to the distance it has covered means that; s' ∝ s. Thus;
s' = ks
