Velocity-Time Graph

Question 16 in the 2016 HSC Mathematics examination involved calculating the distance travelled by a particle given its velocity as a function of time. The velocity during the first second of the motion was negative. This trapped many students. To find the total distance travelled we must add up the absolute values of all of the areas under the v-t graph. Be careful! If you have done it correctly the answer is 10-4ln2. If you obtain 14-12ln2 this is the change in displacement or the final position of the particle measured from the starting point; this is the length of the arrow from the starting point to the finishing point and is not the distance travelled which is the total amount of ground covered.