Question

Consider these statements written in ordinary language:_______.

Answer 1

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