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″<0.
s ′ s′ is constant
s ′ <0 s′<0
s ′′′ <0 s‴<0
s ′′ >0 s″>0
s ′ =ks s′=ks

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

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