1.1 Let's say a cart's position is given by æ(t) = at³ – Bt. (1) Assume the constants, a and ß, are positive. (a) What must be the general type of unit (like length, mass, time, and combinations of these) for each of the constants, a and B? (b) Draw, by hand, a sketch of the two functions at³ and -ßt for t > 0. Add the two curves graphically to get a final sketch of x(t). (c) Calculate the cart's velocity va and acceleration ag. (d) Find an expression for the time t = to at which the cart is momentarily at rest. Check: If a and ß had the values 1 and 27, respectively (in the correct SI units), you would find t = 3 s. (e) Give the expression for the cart's position x(to) at the time t = to. Always simplify your answer, and confirm that the units are correct.

1.1 Let's say a cart's position is given by æ(t) = at³ – Bt. (1) Assume the constants, a and ß, are positive. (a) What must be the general type of unit (like length, mass, time, and combinations of these) for each of the constants, a and B? (b) Draw, by hand, a sketch of the two functions at³ and -ßt for t > 0. Add the two curves graphically to get a final sketch of x(t). (c) Calculate the cart's velocity va and acceleration ag. (d) Find an expression for the time t = to at which the cart is momentarily at rest. Check: If a and ß had the values 1 and 27, respectively (in the correct SI units), you would find t = 3 s. (e) Give the expression for the cart's position x(to) at the time t = to. Always simplify your answer, and confirm that the units are correct.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter1: Units And Measurement

Section: Chapter Questions

Problem 79P: Perform the following calculations and express your answer using the correct number of significant...

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