Question

changes in velocity you learned that acceleration is a change in an objects velocity. one way to change an objects velocity is to change its speed. if the net force acting on a moving object is in the direction that an object is moving, the object speeds up. when the net force on an object is opposite the direction the object moves, the object slows down. that is why a sliding object will eventually come to rest. the net force—friction—opposes the motion of the object, causing it to slow down and stop. another way to change an objects velocity is to change its direction. think about a tennis ball hit by a racquet. the net force exerted on the ball by the racquet causes the ball to move back toward the opponent who served it. read the diagram the diagram shows the net force (f) acting on cart with a mass (m). it also show the acceleration (a) of the cart. draw the acceleration arrow for the cart that experiences a net force of 3f. what is the magnitude of the arrow? explain your answer

Explanation:

Step1: Recall Newton's second - law

Newton's second - law is $F = ma$, where $F$ is the net force, $m$ is the mass and $a$ is the acceleration.

Step2: Analyze the given cases

When the net force is $F$, the acceleration is $a$ (i.e., $F=ma$). When the net force is $2F$, the acceleration is $2a$ (since $2F = m(2a)$).

Step3: Find the acceleration for net force $3F$

If $F = ma$, then for a net force of $3F$, we have $3F=m\times a_{new}$. Solving for $a_{new}$, we get $a_{new}=3a$.

Answer:

The magnitude of the acceleration arrow for a net force of $3F$ is $3a$. This is because according to Newton's second - law $F = ma$, when the mass $m$ is constant, the acceleration $a$ is directly proportional to the net force $F$. So if the net force is tripled from $F$ to $3F$, the acceleration is also tripled from $a$ to $3a$.