Finding Displacement and Velocity at a Given Time

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To find displacement and velocity at t=5 for the given functions, the first function s(t) = 3t + 7 yields a displacement of 22 meters and a constant velocity of 3 m/s. The second function s(t) = t^3 - 2t^2 + 4t - 1 results in a displacement of 94 meters at t=5. To find velocity, the derivative of the displacement function must be calculated. The discussion highlights the need for calculus in determining velocity from the displacement equations, emphasizing that simply substituting values is insufficient. Understanding the relationship between displacement and velocity is crucial for solving such problems effectively.
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Homework Statement


For each function, find an expression for the velocity and the value of the displacement and velocity at t=5. Displacement is in metres and time is in seconds.

Homework Equations


A)[/B] s(t) = 3t + 7

B) s(t) = t3 - 2t2 + 4t - 1

The Attempt at a Solution



A) [/B]s(t) = 3t + 7
s(5) = 3(5) + 7
= 22 m/s

B) s(t) = t3 - 2t2 + 4t - 1
s(5) = 53 - 2(5) + 4(5) - 1
=94 m/s

 
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MiniOreo1998 said:

Homework Statement


For each function, find an expression for the velocity and the value of the displacement and velocity at t=5. Displacement is in metres and time is in seconds.

Homework Equations


A)[/B] s(t) = 3t + 7

B) s(t) = t3 - 2t2 + 4t - 1

The Attempt at a Solution



A) [/B]s(t) = 3t + 7
s(5) = 3(5) + 7
= 22 m/s

B) s(t) = t3 - 2t2 + 4t - 1
s(5) = 53 - 2(5) + 4(5) - 1
=94 m/s
s usually denotes position or displacement, not velocity. How do you find velocity from displacement?

Remember, the problem is asking you to find both displacement and velocity at a given time, t.

Hint: You posted this problem in the Calculus HW forum, yet you used no calculus. Didn't you find that a little odd?
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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