Zadanie 2b
Find the displacement s(t).
Calculus of motion
Connect displacement, velocity and acceleration through calculus and distinguish signed displacement from total distance.
Tę umiejętność sprawdza 45 zadań wzorowanych na arkuszach IB z lat 2022–2026.
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Zadanie 2b
Find ds/dt and d²s/dt² and thereby verify the restoring-acceleration equation.
Zadanie 2c
(i) Use the chain rule to establish a = v dv/ds on a monotone motion branch. (ii) Solve the resulting differential equation to prove v2 = n2(A2 − s2). (iii) Hence or otherwise find the maximum speed.
Zadanie 2e
On the branch moving in the positive direction, write the positive velocity as v₊(s). For −A<s<A, the density has form fS(s) = k/v+(s) with k>0. Find k.
Zadanie 3a
Find the initial velocity.
Zadanie 3b
Find the total distance travelled during the first six seconds.
Zadanie 3c
Find the time when acceleration is 17 m/s².
Zadanie 5a
Find its maximum displacement on this interval.
Zadanie 5b
Find the time intervals on which acceleration is negative.
Zadanie 5a
Find its maximum speed over this interval.
Zadanie 5b
Find the total distance travelled during these 5.5 seconds.
Zadanie 5c
Find the acceleration when the shuttle reverses direction for the second time after it starts.
Zadanie 10a
(i) State u(1). (ii) Find the time when the first cart’s velocity is 4 m/s.
Zadanie 10b
Find the time when the first cart’s acceleration is 3 m/s2.
Zadanie 10c
(i) Find . (ii) Explain why this limit is not an attained trial velocity.
Zadanie 10d
The cart modelled by u finishes first. How far is the other cart from its endpoint at that instant?
Zadanie 10a
State the initial speed of (i) A; (ii) B.
Zadanie 10b
Find (i) when the speeds first agree; (ii) that common speed.
Zadanie 10c
Find d(t), using d(0)=75.
Zadanie 10d
Hence find when B first reaches A.
Zadanie 10e
Find the distance B travels before the first meeting.
Zadanie 10a
Find (i) the maximum displacement; (ii) the maximum velocity, over t≥0.
Zadanie 10b
Find (i) the minimum value of s(t) for t≥0; (ii) s(4.6).
Zadanie 10c
Hence find the total distance travelled during the first 4.6 seconds.
Zadanie 10d
State the first positive time T at which the stage crosses the reference mark.
Zadanie 10e
The stage crosses the reference mark at T,2T,3T,… . Let uₙ be its greatest distance from the mark during (n−1)T<t<nT. These distances form a geometric sequence. Find (i) its common ratio; (ii) the total distance travelled if the model continues indefinitely.
Zadanie 4a
Find the first time at which the stage changes direction.
Zadanie 4b
Find the interval on which its displacement is increasing.
Zadanie 4c
Find its displacement at t=12.
Zadanie 4a
Find v(2.3).
Zadanie 4b
Find the maximum velocity on the given time interval.
Zadanie 4c
Find the acceleration when the carriage changes direction.
Zadanie 5a
Find t1.
- Materiał graficzny
Zadanie 5b
Find t2.
- Materiał graficzny
Zadanie 5c
Find the distance travelled between t1 and t2.
- Materiał graficzny
Zadanie 4a
Find q.
Zadanie 4b
Find the total distance travelled from t=0 to t=q.
Zadanie 4a
Find q.
Zadanie 4b
Find the total distance travelled from t=0 to t=q.
Zadanie 4a
Find the time when the particle is at rest.
Zadanie 4b
Find its acceleration when it changes direction.
Zadanie 4c
Find its total distance travelled over the given interval.
Zadanie 5a
Find when it changes direction.
Zadanie 5b
Find all times when acceleration is −3 m/s².
Zadanie 5c
Find its acceleration when its speed is greatest.