Physics
Physics
Problem
A particle moving in a straight line has the following velocity–time description: • It accelerates uniformly from 0 to 20 m/s in the first 5 s. • It then maintains 20 m/s for the next 3 s. • It finally decelerates uniformly to −10 m/s in the subsequent 4 s. a. (i) Determine the particle’s displacement during the entire 12 s interval. b. (ii) Determine the total distance travelled in this interval.Intuitive explanation
The key here is recognizing that a velocity–time graph tells you everything about motion: the slope gives acceleration, and the area under the curve gives displacement. Break the motion into three distinct phases, calculate the acceleration for each, then use the area method to find total displacement—this visual approach is much cleaner than juggling multiple kinematic equations separately.
Intuitive explanation
The key here is recognizing that a velocity–time graph tells you everything about motion: the slope gives acceleration, and the area under the curve gives displacement. Break the motion into three distinct phases, calculate the acceleration for each, then use the area method to find total displacement—this visual approach is much cleaner than juggling multiple kinematic equations separately.