Analysis and Approaches for IBDP Maths Ebook 1 | страница 212

Your Practice Set – Analysis and Approaches for IBDP Mathematics
71
Paper 2 Section B – Problems in kinematics
Example
A particle moves in a straight line. Its velocity,
v ms
� 1
, at time t seconds, is given by
v
�t
� .
3
�( t� 3) , for 0 6
(a) Find the velocity of the particle when t � 2.
(b)
(c)
(d)
(e)
Find the value of t for which the particle is at rest.
Find the total distance the particle travels during the first six seconds.
Show that the acceleration of the particle is given by
a
2
� � .
3( t 3)
Find all possible values of t for which the velocity and acceleration are both
positive.
[2]
[3]
[3]
[3]
[4]
Solution
(a) v (2)
(M1) for valid approach
3
�(2 � 3)
-1
�� 1ms
A1 N2
(b) vt ( ) � 0
(R1) for zero velocity
(c)
3
( t �3) � 0
t �3� 0
(A1) for correct cube root
t � 3
A1 N2
The total distance travelled
6
� � v( t) dt
(M1) for valid approach
0
6
( t�3)
3
d
0
� � t
(A1) for correct formula
� 40.5 m
A1 N3
(d) at ()
� v�()
t
M1
2
�3( t � 3) (1)
A2
2
�3( t � 3)
AG N0
[2]
[3]
[3]
[3]
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