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Maths AS level

A particle is moving in a straight line. Its
position r at time t is given by
r = 18 − 24t + 9t
2 − t3
0 ⩽ t ⩽ 5
(i) Find the velocity v at time t and
the values of t for which v = 0. I did this already..
(ii) Find the position of the particle at
those times. IK this it is -2m for 2 sec and 2m for 4 secs
(iii) Find the total distance travelled in
the interval 0 ⩽ t ⩽ 5. I drew a position time graph and subtracted between 2sec and 0 secs and added them to the difference between the distance between 4 sec and 5 secs and it was in absolute value ofc,and all i get was 24m , instead of 28m (answer of the book) so i dont know if im doing sth wrong or no..

(edited 3 years ago)

Reply 1

Pangol

Original post by lucydales

There's no need to sketch a graph, unless you are told you have to. It is easy to see that when t = 0, r = 18, and as you say, when t = 2 (the first time it is at rest), r = -2. So the distance travelled in the first two seconds is 20 m. Now do the same for the period from t = 2 to t = 4, and from t = 4 to t = 5.