A particle moving in a straight line covers half of distance with a speed of 3m/s the other half of the distance is covered with two equal intervals of time with speed of 4.5m/s and 7.5m/s respectively find the average speed of this particle during his motion
Answers
Given that,
First half of a distance is covered with speed = 3 m/s
The other half of a distance is covered in 2 equal time intervals at speed of 4.5 M second and 7.5 seconds respectively
Let the total distance covered be 2 x.
Let t be the time taken the first half of the distance.
t = \dfrac{x}{3}t=
3
x
Let the other half of a distance be covered in two equal intervals of time.
x=4.5t'+7.5t'x=4.5t
′
+7.5t
′
x=12t'x=12t
′
t'=\dfrac{x}{12}t
′
=
12
x
The total time is
t''=t+2t't
′′
=t+2t
′
t''=\dfrac{x}{3}+2\times\dfrac{x}{12}t
′′
=
3
x
+2×
12
x
t''=\dfrac{x}{3}+\dfrac{x}{6}t
′′
=
3
x
+
6
x
The average speed is equal to the total distance divided by the total time.
v_{avg}=\dfrac{2x}{\dfrac{x}{3}+\dfrac{x}{6}}v
avg
=
3
x
+
6
x
2x
v_{avg}=4 m/sv
avg
=4m/s
Hence, The average speed of particle during this motion is 4 m/s.