A body of mass 'm' moving along a straight line covers half the distance with a speed of 2 ms-1. The remaining half of the distance is covered in two equal time intervals with a speed of 3 ms-1 and 5 ms-1 respectively. The average speed of the particle for the entire journey is

Question

A body of mass 'm' moving along a straight line covers half the distance with a speed of 2 ms-1. The remaining half of the distance is covered in two equal time intervals with a speed of 3 ms-1 and 5 ms-1 respectively. The average speed of the particle for the entire journey is (A) (8/3) ms-1 (B) (4/3) ms-1 (C) (16/3) ms-1 (D) (3/8) ms-1

Tardigrade Admin · Accepted Answer

Let the total distance travelled by the body is

2 S

. If

t_{1}

is the time taken by the body to travel first half of the distance, then

t_{1} = \frac{s}{2}

Let

t_{2}

be the time taken by the body for each time interval for the remaining half journey.

∴ S = 3 t_{2} + 5 t_{2} = 8 t_{2}

So, average speed

= \frac{Total distance travelled}{Total time taken}

= \frac{2 S}{t _{1} + 2 t _{2}}

= \frac{2 S}{\frac{S}{2} + \frac{S}{4}}

= \frac{8}{3} m s^{- 1}

$\frac{8}{3} m s^{- 1}$

$\frac{4}{3} m s^{- 1}$

$\frac{16}{3} m s^{- 1}$

$\frac{3}{8} m s^{- 1}$

Q. A body of mass ′m′ moving along a straight line covers half the distance with a speed of 2ms−1. The remaining half of the distance is covered in two equal time intervals with a speed of 3ms−1 and 5ms−1 respectively. The average speed of the particle for the entire journey is

38​ms−1

34​ms−1

316​ms−1

83​ms−1

$\frac{8}{3} m s^{- 1}$

$\frac{4}{3} m s^{- 1}$

$\frac{16}{3} m s^{- 1}$

$\frac{3}{8} m s^{- 1}$