Question

assuming the collision lasts 0.01 s, which statements are true? choose two correct answers.
the acceleration of object 1 is (-50 \frac{\text{m}}{\text{s}^2}).
the acceleration of object 2 is (50 \frac{\text{m}}{\text{s}^2}).
the acceleration of object 1 is (150 \frac{\text{m}}{\text{s}^2}).
the acceleration of object 1 is (-150 \frac{\text{m}}{\text{s}^2}).
the acceleration of object 2 is (-50 \frac{\text{m}}{\text{s}^2}).

Explanation:

To solve this, we need to recall the formula for acceleration, \( a=\frac{\Delta v}{\Delta t} \), where \( \Delta v = v_f - v_i \) (final velocity - initial velocity) and \( \Delta t \) is the time interval. However, since the initial and final velocities of the objects are not provided in the question, we assume this is a common problem where (for example, in a typical collision problem with given velocity changes) we can analyze the options:

Analyzing each option:

1. Option 1: Acceleration of object 1 is \( -50 \frac{m}{s^2} \)

If we assume \( \Delta v \) for object 1 is \( -0.5 \, m/s \) (for example) and \( \Delta t = 0.01 \, s \), then \( a=\frac{-0.5}{0.01}=-50 \, m/s^2 \). This is plausible.

1. Option 2: Acceleration of object 2 is \( 50 \frac{m}{s^2} \)

By Newton’s third law, forces in a collision are equal and opposite, so accelerations ( \( a = F/m \)) should also be related by mass, but if we assume masses are equal (or velocity changes are opposite in sign but magnitude leads to this), this could hold. However, let's check the other options.

1. Option 3: Acceleration of object 1 is \( 150 \frac{m}{s^2} \)

This would require a large positive \( \Delta v \), which is inconsistent with typical collision deceleration (or acceleration) unless specific velocities are given, so this is unlikely.

1. Option 4: Acceleration of object 1 is \( -150 \frac{m}{s^2} \)

Similar to above, a large negative acceleration would require a large \( \Delta v \), which is not implied here.

1. Option 5: Acceleration of object 2 is \( -50 \frac{m}{s^2} \)

If object 1 has \( -50 \, m/s^2 \), and forces are equal and opposite, object 2’s acceleration should have the opposite sign (if masses are equal) or a sign based on mass, but this would contradict the "two correct" requirement if paired with option 1.

Correct Answers (Typical Collision Problem Assumptions):

Assuming standard collision dynamics (equal and opposite forces, and solving for acceleration with \( \Delta t = 0.01 \, s \)):

• The acceleration of object 1 is \( -150 \frac{m}{s^2} \) (if \( \Delta v = -1.5 \, m/s \), \( a=\frac{-1.5}{0.01}=-150 \, m/s^2 \)) and the acceleration of object 2 is \( 50 \frac{m}{s^2} \) (if \( \Delta v = 0.5 \, m/s \), \( a=\frac{0.5}{0.01}=50 \, m/s^2 \)) – or vice versa. Wait, perhaps the intended correct answers are:

(Note: Since the original problem likely has context about initial/final velocities, but based on common problems, the two correct answers are often:

• The acceleration of object 1 is \( -150 \frac{m}{s^2} \)
• The acceleration of object 2 is \( 50 \frac{m}{s^2} \)

Or:

• The acceleration of object 1 is \( -50 \frac{m}{s^2} \)
• The acceleration of object 2 is \( 50 \frac{m}{s^2} \)

But to resolve, we re-express:

Using \( a = \frac{v_f - v_i}{\Delta t} \). Suppose for object 1: \( v_i = 1.5 \, m/s \), \( v_f = 0 \, m/s \), \( \Delta t = 0.01 \, s \). Then \( \Delta v = 0 - 1.5 = -1.5 \, m/s \), so \( a = \frac{-1.5}{0.01} = -150 \, m/s^2 \).

For object 2: \( v_i = 0 \, m/s \), \( v_f = 0.5 \, m/s \), \( \Delta t = 0.01 \, s \). Then \( \Delta v = 0.5 - 0 = 0.5 \, m/s \), so \( a = \frac{0.5}{0.01} = 50 \, m/s^2 \).

Answer:

The two correct answers are:

• The acceleration of object 1 is \( -150 \frac{m}{s^2} \)
• The acceleration of object 2 is \( 50 \frac{m}{s^2} \)

(Or, if the velocity changes are smaller, the first and second options. But based on typical problem design, the most probable correct options are the one with \( -150 \, m/s^2 \) for object 1 and \( 50 \, m/s^2 \) for object 2.)

(Note: If the problem had specific velocity values, we would calculate precisely. Since they are not provided, we infer from common collision problems.)

Final Answer (selecting the two correct options):

• The acceleration of object 1 is \( -150 \frac{m}{s^2} \)
• The acceleration of object 2 is \( 50 \frac{m}{s^2} \)