A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is

Question

A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is (A) (2 vd vu/vd+vu) (B) √νu vd (C) (vd vu/vd+vu) (D) (vu+vd/2)

Tardigrade Admin · Accepted Answer

Let t1 and t2 be times taken by the car to go from X to Y and then from Y to X respectively. Then, t1+t2=(X Y/vu)+(X Y/vd)=X Y ⋅((vu+vd/vu vd)) Total distance travelled =X Y+X Y=2 X Y Therefore, average speed of the car for this round trip is v av =(2 X Y/X Y((vu+vd)vu vd)) or v av =(2 vu vd/vu+vd)

Q. A car moves from $X$ to $Y$ with a uniform speed $v_{u}$ and returns to $Y$ with a uniform speed $v_{d}$ . The average speed for this round trip is

$\frac{2 v _{d} v _{u}}{v _{d} + v _{u}}$

$ν_{u} v_{d}$

$\frac{v _{d} v _{u}}{v _{d} + v _{u}}$

$\frac{v _{u} + v _{d}}{2}$

Q. A car moves from X to Y with a uniform speed vu​ and returns to Y with a uniform speed vd​. The average speed for this round trip is

vd​+vu​2vd​vu​​

νu​vd​​

vd​+vu​vd​vu​​

2vu​+vd​​

Q. A car moves from $X$ to $Y$ with a uniform speed $v_{u}$ and returns to $Y$ with a uniform speed $v_{d}$ . The average speed for this round trip is

$\frac{2 v _{d} v _{u}}{v _{d} + v _{u}}$

$ν_{u} v_{d}$

$\frac{v _{d} v _{u}}{v _{d} + v _{u}}$

$\frac{v _{u} + v _{d}}{2}$