Question

mission
1
2
3
4
5
object’s initial velocity
0 cm/s
2 cm/s right
5 cm/s left
5 cm/s right
3 cm/s left
change in velocity (speed up, slow down, start, stop, change direction)
force direction
force strength
change in velocity (cm/s)

Explanation:

Step1: Analyze Mission 1

Initial velocity is \(0\) cm/s. To start moving, the change in velocity will be equal to the final velocity (since initial is \(0\)). The force direction should be the direction of motion. Let's assume it starts moving right with some speed, say if it starts with \(2\) cm/s right (like Mission 2 but starting from 0), but let's take Mission 1: initial velocity \(0\) cm/s. If we want it to start moving, the change in velocity is the final velocity. Let's say force direction is right, force strength causes a change. But maybe the table is to fill for each mission. Let's take Mission 1:

Initial velocity: \(0\) cm/s. Change in velocity: start (so from \(0\) to, say, if it starts moving right with \(2\) cm/s? Wait, Mission 2 has initial \(2\) cm/s right. Maybe Mission 1: change in velocity is "start", so force direction: let's say right (to start moving right), force strength: enough to start, change in velocity: \(2\) cm/s right (similar to Mission 2 but starting from 0). Wait, maybe the table is about relating force to change in velocity (acceleration, since \(F = ma\), and change in velocity is \(a \times t\)). But maybe the problem is to fill the table. Let's take Mission 1:

- Change in velocity: start (so from \(0\) to, let's say, \(2\) cm/s right, same as Mission 2's initial? No, Mission 2 initial is \(2\) cm/s right. Maybe Mission 1: force direction right, force strength: causes initial velocity \(0\) to become moving, so change in velocity is \(2\) cm/s right (same as Mission 2's initial? No, maybe Mission 1: change in velocity is "start", so force direction: right, force strength: let's say moderate, change in velocity: \(2\) cm/s (since Mission 2 has initial \(2\) cm/s right, maybe Mission 1 starts with that). But maybe the key is that for Mission 1:

Initial velocity: \(0\) cm/s.

Change in velocity: start (so from \(0\) to \(v\), where \(v\) is the final velocity). Let's assume force direction is right (to move right), force strength: let's say the same as Mission 2's force strength (if Mission 2 has initial \(2\) cm/s right, change in velocity maybe speed up or slow down, but Mission 1 is starting).

Wait, maybe the table is for each mission (1 - 5) to fill:

Mission 1:

- Initial velocity: \(0\) cm/s

- Change in velocity: start (so from \(0\) to, say, \(2\) cm/s right, so change in velocity is \(2\) cm/s right)

- Force direction: right (to cause motion to the right)

- Force strength: let's say \(F\) (but maybe numerical, but the table has "Force strength" as a column, maybe qualitative, but the last column is "Change in velocity (cm/s)".

So for Mission 1:

Change in velocity (cm/s): \(2\) cm/s right (since it starts from \(0\) to \(2\) cm/s right, same as Mission 2's initial? Maybe not. Alternatively, maybe the problem is to identify the relationship between force and change in velocity (acceleration). Since \(F = ma\), and change in velocity \(\Delta v = a \times t\), so force causes change in velocity (acceleration). So for each mission, the force direction is the direction of \(\Delta v\), force strength is proportional to \(\Delta v\) (if time is constant).

Step2: Analyze Mission 2

Initial velocity: \(2\) cm/s right. Change in velocity: let's say if it speeds up, then \(\Delta v\) is positive (right), force direction right, force strength more than Mission 1. If it slows down, force direction left. But the table's "Change in velocity" column is (speed up, slow down, start, stop, change direction). Mission 2: initial \(2\) cm/s right. If we want to speed up, force direction right, force strength: causes \(\Delta v = 3\) cm/s right (so final velocity \(5\) cm/s right, like Mission 4? Mission 4 initial is \(5\) cm/s right. Wait, Mission 4 initial is \(5\) cm/s right, change in velocity: maybe speed up to \(6\) cm/s? No, Mission 4 initial is \(5\) cm/s right, change in velocity: "speed up" (so \(\Delta v\) positive right), force direction right, force strength.

Mission 3: initial \(5\) cm/s left. Change in velocity: if it changes direction, force direction right (to slow down left and speed up right), so \(\Delta v\) would be (final velocity - initial velocity). Initial is \(5\) cm/s left (\(-5\) cm/s), final if it's \(3\) cm/s left (\(-3\) cm/s), \(\Delta v = (-3) - (-5) = 2\) cm/s right? No, \(3\) cm/s left is \(-3\), so \(\Delta v = -3 - (-5) = 2\) cm/s (right). But Mission 5 initial is \(3\) cm/s left, change in velocity: maybe slow down left, so force direction right, \(\Delta v = 0 - (-3) = 3\) cm/s right? No, Mission 5 initial is \(3\) cm/s left, change in velocity: "slow down" (so from \(3\) cm/s left to, say, \(0\) cm/s), so \(\Delta v = 3\) cm/s right (since initial is \(-3\), final is \(0\), \(\Delta v = 0 - (-3) = 3\) cm/s right), force direction right, force strength.

But maybe the problem is to fill the table with the correct change in velocity, force direction, force strength, etc. Let's take Mission 1:

- Change in velocity: start (from \(0\) to \(2\) cm/s right)

- Force direction: right

- Force strength: moderate

- Change in velocity (cm/s): \(2\) cm/s right

Mission 2:

- Initial velocity: \(2\) cm/s right

- Change in velocity: speed up (to \(5\) cm/s right? No, Mission 4 initial is \(5\) cm/s right. Wait, Mission 2 initial \(2\) cm/s right, Mission 4 initial \(5\) cm/s right, Mission 3 initial \(5\) cm/s left, Mission 5 initial \(3\) cm/s left.

Maybe the table is about:

- For each mission, determine the change in velocity (type: start, speed up, slow down, stop, change direction), force direction (same as \(\Delta v\) direction or opposite), force strength (proportional to \(\Delta v\) magnitude), and \(\Delta v\) in cm/s.

Let's do Mission 1:

- Initial velocity: \(0\) cm/s

- Change in velocity type: start (since it's moving from rest)

- Force direction: right (to move right)

- Force strength: let's say \(F_1\)

- Change in velocity (cm/s): \(2\) cm/s right (so final velocity \(2\) cm/s right, same as Mission 2's initial)

Mission 2:

- Initial velocity: \(2\) cm/s right

- Change in velocity type: speed up (to \(5\) cm/s right? No, Mission 4 initial is \(5\) cm/s right. Wait, Mission 4 initial \(5\) cm/s right, so maybe Mission 2 speeds up to \(5\) cm/s right? Then \(\Delta v = 5 - 2 = 3\) cm/s right, change in velocity type: speed up, force direction right, force strength \(F_2 > F_1\), change in velocity \(3\) cm/s right.

Mission 3:

- Initial velocity: \(5\) cm/s left

- Change in velocity type: slow down (to \(3\) cm/s left? Mission 5 initial is \(3\) cm/s left), so \(\Delta v = 3 - 5 = -2\) cm/s left (or \(2\) cm/s right), change in velocity type: slow down (since speed decreases from \(5\) to \(3\) cm/s left), force direction right (opposite to motion, to slow down), force strength \(F_3\), change in velocity \(2\) cm/s right (since \(5 - 3 = 2\) cm/s decrease in left velocity, so \(\Delta v = +2\) cm/s right)

Mission 4:

- Initial velocity: \(5\) cm/s right

- Change in velocity type: speed up? No, Mission 4 initial \(5\) cm/s right, Mission 2 initial \(2\) cm/s right, so maybe Mission 4 slows down? Wait, Mission 4's initial is \(5\) cm/s right, Mission 2's initial is \(2\) cm/s right, so maybe Mission 4 speeds up to \(6\) cm/s? No, the table has Mission 4 initial \(5\) cm/s right, Mission 2 initial \(2\) cm/s right, so maybe Mission 2 speeds up to \(5\) cm/s (Mission 4's initial), so \(\Delta v = 5 - 2 = 3\) cm/s right, change in velocity type: speed up, force direction right, force strength \(F_2\), change in velocity \(3\) cm/s right.

Mission 3:

- Initial velocity: \(5\) cm/s left

- Change in velocity type: change direction? No, Mission 3 initial \(5\) cm/s left, Mission 5 initial \(3\) cm/s left, so maybe slow down to \(3\) cm/s left (speed decreases), so force direction right (opposite to motion), change in velocity type: slow down, \(\Delta v = 3 - 5 = -2\) cm/s left (or \(2\) cm/s right), force strength \(F_3\), change in velocity \(2\) cm/s right.

Mission 5:

- Initial velocity: \(3\) cm/s left

- Change in velocity type: stop (to \(0\) cm/s), so \(\Delta v = 0 - 3 = -3\) cm/s left (or \(3\) cm/s right), change in velocity type: stop, force direction right (opposite to motion, to stop), force strength \(F_5 > F_3\) (since \(\Delta v\) magnitude is \(3\) vs \(2\) for Mission 3), change in velocity \(3\) cm/s right.

But maybe the problem is simpler: the last column is "Change in velocity (cm/s)", so for Mission 1:

Initial velocity \(0\) cm/s, if it starts moving with \(2\) cm/s right, then \(\Delta v = 2 - 0 = 2\) cm/s right.

Mission 2: initial \(2\) cm/s right, if it becomes \(5\) cm/s right (Mission 4 initial), then \(\Delta v = 5 - 2 = 3\) cm/s right.

Mission 3: initial \(5\) cm/s left, becomes \(3\) cm/s left (Mission 5 initial), so \(\Delta v = 3 - 5 = -2\) cm/s left (or \(2\) cm/s right).

Mission 4: initial \(5\) cm/s right, if it becomes \(6\) cm/s right? No, maybe Mission 4 is speed up to \(5\) cm/s right from \(2\) cm/s right (Mission 2), but no, Mission 4 initial is \(5\) cm/s right.

Alternatively, maybe the table is already partially filled, but the user needs to complete it. Since the initial question is not clear, but assuming the task is to fill the table, here's a possible completion:

| Mission | Object’s initial velocity | Change in velocity (type) | Force direction | Force strength | Change in velocity (cm/s) |
|---------|---------------------------|---------------------------|-----------------|----------------|---------------------------|
| 1 | 0 cm/s | start | right | moderate | 2 cm/s right |
| 2 | 2 cm/s right | speed up | right | strong | 3 cm/s right |
| 3 | 5 cm/s left | slow down | right | moderate | 2 cm/s right |
| 4 | 5 cm/s right | speed up | right | strong | 1 cm/s right (to 6 cm/s? No, Mission 4 initial is 5, maybe 0? No) | Wait, maybe Mission 4 initial is 5 cm/s right, change in velocity type: slow down, force direction left, \(\Delta v = -3\) cm/s right (to 2 cm/s right), but Mission 2 initial is 2 cm/s right. This is getting confusing. Maybe the key is that force causes change in velocity (acceleration), so direction of force is direction of \(\Delta v\), strength is proportional to \(\Delta v\) magnitude.

Answer:

The table can be filled by relating force (direction and strength) to the change in velocity (type and magnitude) using the relationship \( \boldsymbol{F = ma} \) (force causes acceleration, which is change in velocity over time). For each mission:

• Mission 1: Starts from rest (\(0\) cm/s). Change in velocity type: start (from rest to motion). Force direction: right (to move right). Force strength: moderate (to initiate motion). Change in velocity: \(2\) cm/s right (final velocity \(2\) cm/s right, matching Mission 2’s initial velocity).

• Mission 2: Initial velocity \(2\) cm/s right. Change in velocity type: speed up (to \(5\) cm/s right, like Mission 4’s initial). Force direction: right (same as motion). Force strength: strong (to increase speed). Change in velocity: \(3\) cm/s right (\(5 - 2 = 3\) cm/s).

• Mission 3: Initial velocity \(5\) cm/s left. Change in velocity type: slow down (to \(3\) cm/s left, matching Mission 5’s initial). Force direction: right (opposite to motion, to reduce speed). Force strength: moderate (small speed decrease). Change in velocity: \(2\) cm/s right (\(3 - 5 = -2\) cm/s left \(= 2\) cm/s right).

• Mission 4: Initial velocity \(5\) cm/s right. Change in velocity type: slow down (to \(2\) cm/s right, matching Mission 2’s initial). Force direction: left (opposite to motion, to reduce speed). Force strength: strong (large speed decrease). Change in velocity: \(3\) cm/s left (\(2 - 5 = -3\) cm/s right \(= 3\) cm/s left).

• Mission 5: Initial velocity \(3\) cm/s left. Change in velocity type: stop (to \(0\) cm/s). Force direction: right (opposite to motion, to stop). Force strength: strong (to halt motion). Change in velocity: \(3\) cm/s right (\(0 - 3 = -3\) cm/s left \(= 3\) cm/s right).

(Note: The exact values depend on the intended final velocity for each mission, but the key is that force direction matches the direction of the change in velocity, and force strength is proportional to the magnitude of the change in velocity.)