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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.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Help me with answering question (d) and (e)

1.1 Let's say a cart's position is given by x(t) at3 – Bt. (1) - Assume the constants, a and B, 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 at and –ßt for t > 0. Add the two curves graphically to get a final sketch of x(t). (c) Calculate the cart's velocity vr and acceleration ar. (d) Find an expression for the time t = to at which the cart is momentarily at rest. Check: If a and B 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.
Transcribed Image Text:1.1 Let's say a cart's position is given by x(t) at3 – Bt. (1) - Assume the constants, a and B, 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 at and –ßt for t > 0. Add the two curves graphically to get a final sketch of x(t). (c) Calculate the cart's velocity vr and acceleration ar. (d) Find an expression for the time t = to at which the cart is momentarily at rest. Check: If a and B 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.
Expert Solution
Step 1

given that,x(t)=αt3-βt

here x represents position.so, the units of α and βare ms3 and ms respectively

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