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IB Mathematics SL Calculus: Kinematics

Question 1

The following diagram shows the graphs of the displacement, velocity and acceleration of a moving object as functions of time, t.

(a) Complete the following table by noting which graph A, B or C corresponds to each function.

Function Graph
displacement
acceleration

(b) Write down the value of t when the velocity is greatest.

Question 2

In this question s represents displacement in metres and t represents time in seconds.
The velocity v m/s of a moving body is given by vt= 40-at a where a is a non-zero constant.
(a) (i) If
s =100 when t = 0, find an expression for s in terms of a and t.
(ii) If
s = 0 when t = 0, write down an expression for s in terms of a and t.
Trains approaching a station start to slow down when they pass a point P. As a train slows down, its velocity is given by v=40-at, where t = 0 at P. The station is 500 m from P.
(b) A train M slows down so that it comes to a stop at the station.

      Find the time it takes train M to come to a stop, giving your answer in terms of a.
(ii) Hence show that
a = 8/5.
(c) For a different train N, the value of a is 4.
Show that this train will stop
before it reaches the station.