Question

A particle moving in a straight line covers half the distance with a speed of 3 m/s. The other half of the distance is covered in two equal time intervals with speeds of 4.5 m/s and 7.5 m/s respectively. The average speed of the particle during this motion is

विकल्प

• 4.0 m/s

• 5.0 m/s

• 5.5 m/s

• 4.8 m/s

Answer 1

4.8 m/s

Explanation:

Let the total distance be s. The time taken to travel  the first half, i.e., `s/2` is t₁ = `(s/2)/3 = s/6`

Let t₂ be the time taken to cover a distance s₁  with speed 4.5 m/s and t₃ that to cover distance s₂ with speed 7.5 m/s.

Then s₁ = 4.5 t₂ and s₂ = 7.5 t₃

Now s₁ + s₂ = `s/2` and t₂ = t₃  .....(given)

Therefore `s/2` = s₁ + s₂ = (4.5 + 7.5)t₂

or t₂ = `s/24`

∴  Total time taken t = t₁ + t₂ = `s/6 + s/24 = (5s)/24`

∴ Average speed = `"distance"/"time" = s/((5s)/24) = 24/5` = 4.8 m/s