The speed, V (km/h), of a car at time t (seconds) is given by 75 - 15 sin (t-60) 120 (t-60) 120 V = f(t) 2+ sin where 0 ≤ t ≤ 120. (a) We want to know when the car will reach a certain speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f-¹(t). (b) Write down the domain of f-¹(t). (c) Plot f(t) from t = 0 tot = 120 and then plot f-¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b). (d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). (e) When will the speed of the car be equal to 27 km/h? Use the inverse function you found in part (a) to help you answer this.
The speed, V (km/h), of a car at time t (seconds) is given by 75 - 15 sin (t-60) 120 (t-60) 120 V = f(t) 2+ sin where 0 ≤ t ≤ 120. (a) We want to know when the car will reach a certain speed. Solve for the time t in terms of the speed V, and hence find the formula for the inverse function f-¹(t). (b) Write down the domain of f-¹(t). (c) Plot f(t) from t = 0 tot = 120 and then plot f-¹(t) on the same axes but only for the values of t in the domain of the inverse function found in (b). (d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t). (e) When will the speed of the car be equal to 27 km/h? Use the inverse function you found in part (a) to help you answer this.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Advanced Math
please help with question A and E
Transcribed Image Text:The speed, V (km/h), of a car at time t (seconds) is given by
π(t - 60)
120
(t-60)
120
V = f(t)=
75 - 15 sin
2 + sin
where 0 ≤ t ≤ 120.
(a) We want to know when the car will reach a certain speed. Solve for the time t in terms of the
speed V, and hence find the formula for the inverse function f-¹(t).
(b) Write down the domain of f-¹(t).
(c) Plot f(t) from t = 0 to t = 120 and then plot f-¹(t) on the same axes but only for the values
of t in the domain of the inverse function found in (b).
(d) Describe the geometric relationship that you can see when you consider both f(t) and f-¹(t).
(e) When will the speed of the car be equal to 27 km/h?
Use the inverse function you found in part (a) to help you answer this.
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