Final answer:
The v-t graph can be plotted by dividing the boy's motion into intervals. The acceleration can be calculated for each interval. The total distance traveled by the boy can be found by calculating the area under the velocity-time graph.
Step-by-step explanation:
a. The velocity-time (v-t) graph can be plotted as follows:
For the first 2 seconds, the boy runs at 8m/s starting from rest, so the graph is a straight line with a positive gradient:
(0,0) - (2,8)
For the next 2 seconds, the boy walks at a constant speed, so the graph is a straight horizontal line:
(2,8) - (4,8)
For the next 2 seconds, the boy slows down to 4m/s, so the graph is a straight line with a negative gradient:
(4,8) - (6,4)
Finally, the boy walks at a constant speed for 4 seconds and comes to rest in 2 seconds, so the graph is a straight horizontal line followed by a straight line with a negative gradient:
(6,4) - (10,4) - (12,0)
b. The acceleration in each interval can be calculated using the formula:
acceleration = (final velocity - initial velocity) / time
For the first interval, the acceleration is:
acceleration = (8 - 0) / 2 = 4 m/s²
For the second interval, the boy walks at a constant speed, so the acceleration is:
acceleration = 0 m/s²
For the third interval, the acceleration is:
acceleration = (4 - 8) / 2 = -2 m/s²
For the fourth interval, the boy walks at a constant speed, so the acceleration is:
acceleration = 0 m/s²
c. To find the distance the boy traveled in the whole time, we can calculate the area under the velocity-time graph. The total distance can be calculated as the sum of the distances traveled in each interval:
Distance = (0.5 * 2 * 8) + (2 * 8) + (0.5 * 2 * 4) + (4 * 4) + (0.5 * 2 * 0) = 32 + 16 + 4 + 16 + 0 = 68 meters