## Explanation

### Changes in the Velocity (Speed) of the Object

When a force is applied to an object, one of the primary ways it can change the motion of the object is by altering its velocity, which refers to both the speed and direction of the object's motion.

$\textbf{Newton's Second Law:} \quad \vec{F} = m \cdot \vec{a}$In cases where the force is applied in the same direction as the object's motion, the object's speed increases. Conversely, if the force is applied in the opposite direction, the object's speed decreases.

### Changes in the Direction of Motion

Forces can also change the direction in which an object is moving. This can happen even if the speed of the object remains constant. For instance, when a car turns a corner, the force exerted by friction between the tires and the road changes the car's direction.

$\textbf{Centripetal Force:} \quad \vec{F}_c = \frac{m \cdot v^2}{r}$In this formula, $m$ is the mass of the object, $v$ is its velocity, and $r$ is the radius of the circular path.

### Inducing Rotational Motion

An applied force can induce **rotational motion** in an object. This is governed by the concept of torque, or the rotational equivalent of force. The equation for torque ($\tau$) is:

where $\vec{r}$ is the radius vector (distance from the axis of rotation to the point where the force is applied) and $\vec{F}$ is the applied force. This torque results in angular acceleration, changing the rotational motion of the object.

**Summary**:

**Changes in speed**: Force can speed up or slow down an object.**Changes in direction**: Forces like friction can alter the path of an object.**Inducing rotational motion**: Torque from applied forces can cause objects to rotate.