NEETPhysicsMotion in One Dimension
A boy walks from his home to a store along a straight path at a constant speed v₁ . He returns to his home along the same path at an unknown constant speed v₂ . If the average speed for his entire round trip is V , which of the following expressions correctly gives v₂ ?
Options
- A2V - v₁
- BV v₁ 2 v₁ + V
- CV v₁ v₁ - V
- DV v₁ 2 v₁ - V
Correct answer
D. V v₁ 2 v₁ - V
Step-by-step solution
Let the distance from home to the store be d . The total distance for the round trip is 2d . Time taken for the outbound journey, t₁ = d v₁ . Time taken for the return journey, t₂ = d v₂ . Total time taken, T = t₁ + t₂ = d v₁ + d v₂ = d ( v₁ + v₂ v₁ v₂ ) . The average speed V for the entire trip is given by total distance divided by total time: V = 2d d ( v₁ + v₂ v₁ v₂ ) = 2 v₁ v₂ v₁ + v₂ . Rearranging the equation to solve for v₂ : V(v₁ + v₂) = 2 v₁ v₂ V v₁ + V v₂ = 2 v₁ v₂ V v₁ = 2 v₁ v₂ - V v₂ V v₁ = v₂(2 v₁ - V