Question

A particle moving in a straight line covers half the distance with speed of 3 metre per second the other half of the distance is covered in two equal time intervals with a speed of 4.5 metre per second and 7.5 metre per second respectively what is the average speed of the particle​

Answer 1

Answer:

The average speed of particle during this  motion is 4 m/s.

Explanation:

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}

Let the other half of a distance be covered in two equal intervals of time.

x=4.5t'+7.5t'

x=12t'

t'=\dfrac{x}{12}

The total time is

t''=t+2t'

t''=\dfrac{x}{3}+2\times\dfrac{x}{12}

t''=\dfrac{x}{3}+\dfrac{x}{6}

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}=4 m/s

Hence, The average speed of particle during this  motion is 4 m/s.

Answer 2

t
1
​
=
3
2
S
​

​
=
6
S
​

2
S
​
=4.5×t
2
​
+7.5t
3
​
⇒12t
2
​
=
2
S
​

We have t
2
​
=t
3
​

Total time t=t
1
​
+t
2
​
+t
3
​
=
6
S
​
+
24
S
​
+
24
S
​
=
4
S
​

Average of
t
S
​
=
4
S
​

S
​
=