Page 50 - Math SL HB Sem 2

Motion in straisht line

distance travelled
h.IlOW: average speed = --------
-
time taken
(t)= =s'(t)
*

Given a velocity function we can determine the displacement function by integration.
From the displacement function we can determine the total distances traveled ln some time
interval act < b.

Example 28: The velocity of an object is v m/s after t seconds, where v = I
- 2 sin 2t.
a) find the object's displacement over the n.rt & seconds. IAns:1.36]
4

b) Find the distance traveled by the object over the fu$+ seconds. Ans:2.73]
I
v4

I
0 th t'tt ? tt/

Example 29 : A rocket starts from rest and accelerates such that its acceleration is given by the
formula a(t) = 3t + t2; 0 StS 10 where distances are measuredln metres
and time in seconds. Find the distance traveled in the first ten seconds ofthe
rocket's motion.
lens: t333 /3)