Question

forces unit 1 test review which of the following is true if the student were to apply the same force to each cart for the same amount of time? select the two correct answers. a. the unloaded cart would have a slower acceleration. b. the unloaded cart would have a quicker acceleration. c. the unloaded cart would reach a higher speed than the loaded cart. d. the loaded cart would reach a higher final speed than the unloaded cart.

Explanation:

To solve this, we use Newton's second law (\(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration). If the same force is applied to two cars (let's assume different masses, e.g., a loaded car has more mass than an unloaded one), we analyze each option:

Step 1: Analyze Option A

From \(a=\frac{F}{m}\), if the loaded car has more mass (\(m_{loaded}>m_{unloaded}\)) and \(F\) is the same, then \(a_{loaded}=\frac{F}{m_{loaded}} < \frac{F}{m_{unloaded}}=a_{unloaded}\). So the loaded car has a smaller acceleration, not a slower acceleration (acceleration is the rate of change of velocity, not speed itself). This is incorrect.

Step 2: Analyze Option B

Using \(a=\frac{F}{m}\), since \(m_{loaded}>m_{unloaded}\) and \(F\) is constant, \(a_{loaded}

Step 3: Analyze Option C

Speed depends on acceleration and time (\(v = u + at\), where \(u\) is initial speed). Without knowing initial speed (\(u\)) or time (\(t\)), we cannot conclude the unloaded car “would need a greater speed” (speed is not directly determined by mass alone with the same force). This is incorrect.

Step 4: Analyze Option D

Final speed (\(v = u + at\)) depends on initial speed (\(u\)), acceleration (\(a\)), and time (\(t\)). With \(u\) and \(t\) unknown, we cannot say the loaded car “would reach a slower final speed.” This is incorrect.

Answer:

B. The unloaded car would have a greater acceleration.