A particle moves along a straight track for seconds
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A particle moves along a straight track for 0≤t≤8 seconds. Its velocity v(t) (in meters per second) is described verbally as follows:
• v(t)>0 and decreases linearly from 4 to 0 on 0≤t≤3.
• v(t)<0 and decreases linearly from 0 to −3 on 3≤t≤5.
• v(t)>0 and increases linearly from 0 to 5 on 5≤t≤8.
Assume straight‐line motion with the origin at the particle’s starting position.
(a) State an integral expression that gives the particle’s net displacement on the interval 0≤t≤8. Do not evaluate.
(b) State an integral expression that gives the particle’s total distance traveled on the same interval. Do not evaluate.
(c) Explain, with reference to the given information, why the numerical values of the two quantities in parts (a) and (b) are different.