AP Calculus BC : 1.1 Introducing Calculus: Can Change Occur at  an Instant? Exam Style questions with Answer- MCQ

Question

The position of a particle moving to the right on the x -axis is given by x(t) , where x(t) is measured in centimeters and  t is measured in seconds for  0≤t≤50 . If y=x(t) is a linear function, which of the following would most likely give the best estimate of the speed of the particle, in centimeters per second, at time  t=10  seconds?

A x(10)

B  \(\frac{x(10)}{10}\)

C x(11)-x(9)

D The slope of the graph of y=x(t)

Answer/Explanation

Ans:D

This gives the exact value of the speed of the particle at any time t  in the interval [0,50

Question

A model rocket leaves the ground at time t=0 and travels straight up from the ground. The height, in feet, of the rocket above the ground is given by  y(t), where t is measured in seconds for 0≤t≤120 .Values of y(t) for selected values of t are given in the table above. Of the following values of  t,at which value would the velocity of the rocket most likely be greatest based on the data in the table?
A t=20
B t=40
C t=60
D t=80

Answer/Explanation

Ans:D

Question

A particle is moving on the x

-axis and the position of the particle at time 

is given by x(t), whose graph is given above. Which of the following is the best estimate for the speed of the particle at time  t=

?

A 0

B 5

C \(\frac{20}{3}\)

D 20

Answer/Explanation

Ans:A

At time t=4

, the particle is stationary at the position x

(t)=20

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