Calculate average speed/acceleration for the given function

Alexanddros81 · Nov 9, 2018

Homework Statement

Serway Physics Chapter 2

20. An object moves along the x-axis according to the equation ##x=3.00t^2 - 2.00t+3.00##,
where x is in meters and t is in seconds. Determine (a) the average speed between
t=2.00s and t=3.00s, (b) the instantaneous speed at t = 2.00s and at t=3.00s, (c) the average acceleration
between t=2.00s and t=3.00s and (d) the instantaneous acceleration at t=2.00s and t=3.00s.
(e) At what time is the object at rest?

Homework Equations

The Attempt at a Solution

Handwritten working for part c to e of a physics problem: v_x(t) = 6.00t - 2.00 plotted, average acceleration from t=2s to t=3s equals 6 m/s^2, acceleration at A and B equals 6 m/s^2, and v_x(t)=0 gives t = 0.33 s.

Graph of x (m) against t (s) for x = 3t² − 2t + 3, a parabola with minimum near t = 0.3. Two labelled points: A = (2, 11) and B = (3, 24), with a red secant line joining them and green tangent lines at each point.

Graph of U (m/s) against t (s) showing a straight rising line, with labelled points A = (2, 10) and B = (3, 16) marked on it.

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In part (a) I calculated average velocity but it asks for the average speed which is
given by ##v_{avg} = \frac {d} {Δt}## where d is distance traveled between 2 and 3 seconds, which is
13m. So average speed is the same as average velocity in this case.

Is the above correct?

DrClaude · Nov 9, 2018

It all looks ok.

Calculate average speed/acceleration for the given function

Homework Statement

Homework Equations

The Attempt at a Solution

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