The boy traveled a total distance of 44 meters.
Let's analyze the motion of the boy in different intervals and plot the velocity-time (v-t) graph, find the acceleration in each interval, and calculate the total distance traveled.
a. Velocity-Time (v-t) Graph:
First 2 seconds (Running at 8 m/s from rest):
Initial velocity (u) = 0 m/s
Final velocity (v) = 8 m/s
Time (t) = 2 seconds
Next 2 seconds (Walking at constant speed):
Initial velocity (u) = 8 m/s (from the previous interval)
Final velocity (v) = 8 m/s (constant speed)
Time (t) = 2 seconds
Next 2 seconds (Slowing down to 4 m/s):
Initial velocity (u) = 8 m/s
Final velocity (v) = 4 m/s
Time (t) = 2 seconds
Next 4 seconds (Walking at constant speed):
Initial velocity (u) = 4 m/s (from the previous interval)
Final velocity (v) = 4 m/s (constant speed)
Time (t) = 4 seconds
Last 2 seconds (Coming to rest):
Initial velocity (u) = 4 m/s
Final velocity (v) = 0 m/s
Time (t) = 2 seconds
Now, let's plot the v-t graph based on this information.
b. Acceleration in Each Interval:
Acceleration (a) is given by the formula:
a= Δv/Δt
First 2 seconds:
a= 8m/s−0m/s/2s−0s = 8m/s/2s =4m/s^2
Next 2 seconds:
Acceleration is zero since the speed is constant.
Next 2 seconds:
a= 4m/s−8m/s/2s−0s= −4m/s/2s =−2m/s^2
Next 4 seconds:
Acceleration is zero since the speed is constant.
Last 2 seconds:
a= 0m/s−4m/s/ 2s−0s = −4m/s/2s =−2m/s^2
c. Total Distance Traveled:
To find the total distance traveled, we need to calculate the distance in each interval and sum them up.
First 2 seconds:
s_1 =ut+ 1/2 at^2 =0×2+ 1/2 ×4×(2^2 )=4m
Next 2 seconds:
s_2 =ut+ 1/2 at^2 =8×2+ 1/2 ×0×(2^2 )=16m
Next 2 seconds:
s_3 =ut+ 1/2 at^2 =8×2+ 1/2 ×(−2)×(2^2 )=12m
Next 4 seconds:
s_4 =ut+ 1/2 at^2 =4×4+ 1/2 ×0×(4^2 )=16m
Last 2 seconds:
s_5 =ut+ 1/2 at^2 =0×2+ 1/2 ×(−2)×(2^2 )=−4m
Total Distance:
Total Distance=s_1 +s_2 +s_3 +s_4 +s_5 =4+16+12+16−4=44m
So, the boy traveled a total distance of 44 meters.
Question
1.A boy runs at 8m/s starting from rest for 2 sec, then he walks at a constant speed for 2sec and then slows down to 4m/sec in 2 sec and finally he walks with constant speed for 4 sec and come to rest in 2 sec a. Plot the v-t graph for the motion b. Find the acceleration in each interval c. How far the boy traveled in the whole time