Final answer:
To find the displacement and distance traveled by a particle during a time interval, you need to determine the particle's positions at each endpoint of the interval. The displacement is the difference in position, while the distance traveled is the total length of the path taken by the particle. The particle's position and the length of the straight line segments connecting these positions are used to calculate the displacement and distance traveled.
Step-by-step explanation:
To find the displacement and the distance traveled by the particle during the time interval [-2,5], we first need to determine the particle's position at each endpoint of the interval. Let's assume the particle's position at t=-2 is x(-2)=-1 and at t=5 is x(5)=4. The displacement is given by the difference in position: displacement = x(5) - x(-2) = 4 - (-1) = 5 units. The distance traveled is the total length of the path taken by the particle during the interval. In this case, it would be the sum of the lengths of the straight line segments connecting the positions x(-2) and x(5). Since each segment has a length of 1 unit, the distance traveled is 7 units.