Transition Year Maths Example 2:


The manufacturers of a small rocket claim its motion is given by x = 3t 2


+ 2t. Therefore the distance x it will


move in metres can be found by putting the time t into the formula. After three seconds it will move 3(3)2


+ 2(3) = 33 metres.


Using calculus we can find its velocity or acceleration at any time t.


Motion is defined by Velocity is defined by


Acceleration is defined by x = 3t 2


v dx dt


a dv dt


(x) (v) + 2t == t + ==6


Time Distance Velocity Acceleration (t)


t 3t 2 + 2t


0 sec 0 m 1 sec 5 m 2 sec 16 m 3 sec 33 m


6t + 2 2 m/s 8 m/s


14 m/s 20 m/s


(a) 6


6 m/s2 6 m/s2 6 m/s2 6 m/s2


Examine this to see if it is true! • If a car moves 16 m in 2 seconds, its average velocity should be 8 m per sec, and it is 8 m/s after 1 sec, half way between 0 sec and 2 sec.


• If a car moves from 5 m to 33 m in the 2 sec from 1 sec to 3 sec, the average velocity should be


33 ==5 2


–


28 2


14 m/s, and it is after 2 sec.


• If velocity increases from 8 m/s after 1 sec to 14 m/s after 2 sec it is accelerating at 6 m/s per sec ⇒acceleration = 6 m/s2


. 62


140


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