Question 1.10: The velocity (in ms^-1) of a model train which is moving alo...
The velocity (in ms^{-1}) of a model train which is moving along straight rails is
v = 0.3t² – 0.5
Find its displacement from its initial position
i) after time t
ii) after 3 seconds.
i) The displacement at any time is s = \int{v dt}
= \int{(0.3t² – 0.5) dt}
= 0.1 t³ – 0.5t + c
To find the train’s displacement from its initial position, put s = 0 when t = 0.
This gives c = 0 and so s = 0.1t³ – 0.5t.
You can use this equation to find the displacement at any time before the motion changes.
ii) After 3 seconds, t = 3 and s = 2.7 – 1.5.
The train is 1.2 m from its initial position.
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When using integration don’t forget the constant. This is very important in mechanics problems and you are usually given some extra information to help you find the value of the constant.