Question

The position (in thousands of feet) of a car driving along a straight road at time t in minutes is given by the function y = s(t) that is pictured below. У S 14 10 6 2 2 6 10 Let v(t) denote the velocity of the car (in thousands of feet per minute) at timet (in minutes). Which graph A-F is the best representative of the derivative function v'(t)? Evº

need help with last question: which of the following statements are true?

Answer 1

Graph A represents v'(t) v/s t.

From the statements:

A. False, v'(t) is the acceleration of the particle at time t i.e., rate of change of velocity which is positive if velocity increases and negative if it decreases.

B. False, v'(t) is the acceleration of the particle at time t

C. True, when the particle moves with constant velocity, v'(t) is zero but v(t) is not zero.

D. False, v'(t) is negative when velocity of the car is decreasing.

E. True, rate of change of velocity is acceleration. So, v'(t)=acceleration.

G. False, the car moving backward and speeding up has negative v'(t).

Answer 2

E is actually false, v''(t) is acceleration not v'(t) and D is true because decreasing would again be acceleration which is not listed in this problem.