QUIZ #1: CALCULUS 1A (Stankova) Wednesday, January 28, 2004 Section 10:00–11:00 (Voight)

Name:

Please complete the following problem in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. The position of a hydrogen fuel-cell vehicle is given by the values in the following table:

t (seconds) 0 5 10 15 20 25 ; s (feet) 30 150 450 950 1600 2575

(a) Find the average velocity for the time period beginning when t = 5 and lasting:

(i) 15 seconds

(ii) 10 seconds

(iii) 5 seconds

(b) Use the graph of s as a function of t to estimate the instantaneous velocity when t = 5.

QUIZ #1: CALCULUS 1A (Stankova) Wednesday, January 28, 2004 Section 11:00–12:00 (Voight)

Name:

Please complete the following problem in the space provided. You may not use a calculator. You will have 15 minutes to complete the quiz.

Please include all relevant intermediate calculations and explain your work when appropriate.

Problem 1. If a pellet is shot upward by the Mars rover, its height in kilometers after t seconds is given by h = 3t − t^{2}.

(a) Find the average velocity over the given time intervals: (i) [0, 1]

(ii) [0, 0.5]

(iii) [0, 0.1]

(b) Graph the height of the pellet as a function of time; draw the tangent line to the graph at time t = 0.

(c) Find the initial velocity at which the pellet was shot.