A car passes a curve of a road, which has the form of a circle (the angle of rotation is $90^{ \circ}$), with a constant speed $v$ and in time $t$. What is the average force acting on the car during the turn if the mass of the car is $m$?
Decision:
The average force $F_{c}$ over time $t$ causes the same change in the velocity vector $\Delta v$ as the actual force $F(t)$:
$\bar{F_{c}} = \frac{m \Delta \bar{v}}{t}$.
Considering that the velocity vector has rotated by $90^{ \circ}$ at time $t$, while remaining unchanged in magnitude, we obtain the change in velocity
$|\Delta \bar{v}| = \sqrt{2}v$.
The magnitude of the average force
$|\bar{F_{c}}|= \frac{ \sqrt{2} mv}{t}$.
Decision:
The average force $F_{c}$ over time $t$ causes the same change in the velocity vector $\Delta v$ as the actual force $F(t)$:
$\bar{F_{c}} = \frac{m \Delta \bar{v}}{t}$.
Considering that the velocity vector has rotated by $90^{ \circ}$ at time $t$, while remaining unchanged in magnitude, we obtain the change in velocity
$|\Delta \bar{v}| = \sqrt{2}v$.
The magnitude of the average force
$|\bar{F_{c}}|= \frac{ \sqrt{2} mv}{t}$.