Question

force strength and velocity change (continued)
what do you notice about the relationship between the force strength and the size of the velocity change?
if you have time, complete the optional missions 6, 7, and 8, and record your results
mission | 6 | 7 | 8
object’s initial velocity | 0 cm/s | 6 cm/s right | 4 cm/s right
change in velocity (speed up, slow down, start, stop, change direction) | | |
force direction | | |
force strength | | |
change in velocity (cm/s) | | |

Explanation:

Step1: Analyze Mission 6

For Mission 6, initial velocity is \( 0 \, \text{cm/s} \). Let's assume a force is applied (direction and strength to be considered). If we apply a force to start the object moving, say right direction with some strength. The change in velocity would be "start" (from 0 to some speed). Let's say force direction is right, force strength moderate, change in velocity: start (so final velocity - initial velocity = final velocity, let's assume after force, velocity becomes, e.g., \( 2 \, \text{cm/s} \), but maybe the table expects qualitative first. Wait, maybe the problem is about filling the table. Let's take Mission 6:

- Initial velocity: \( 0 \, \text{cm/s} \)
- Change in velocity: start (so from 0, starts moving)
- Force direction: Let's say right (to start moving right)
- Force strength: Let's say 5 (arbitrary, but to show)
- Change in velocity (cm/s): Let's say if force is applied, and object starts moving, change is, e.g., \( 2 \, \text{cm/s} \) (but maybe qualitative, but the table has "Change in velocity (cm/s)". Wait, maybe the problem is to observe the relationship, but the table is for filling. Let's do Mission 6,7,8:

Mission 6:
- Initial velocity: \( 0 \, \text{cm/s} \)
- Change in velocity: start (so speed up from 0)
- Force direction: right (assume)
- Force strength: 5 (example)
- Change in velocity (cm/s): Let's say after force, velocity is \( 2 \, \text{cm/s} \), so change is \( 2 - 0 = 2 \, \text{cm/s} \)

Mission 7:
- Initial velocity: \( 6 \, \text{cm/s} \) right
- Change in velocity: Let's say we apply a force left (to slow down or stop). If force is left, direction left, strength 6 (stronger than Mission 6? Maybe). Change in velocity: slow down (so final velocity less than 6). Let's say final velocity is \( 4 \, \text{cm/s} \), change is \( 4 - 6 = -2 \, \text{cm/s} \) (but magnitude or direction? The table says "Change in velocity (cm/s)". Wait, maybe the problem is to see that force strength affects the change in velocity (Newton's second law: \( F = ma \), so \( \Delta v = a \Delta t \), so force strength (F) is proportional to change in velocity (since \( a = F/m \), so \( \Delta v = (F/m) \Delta t \), so if mass is constant, F is proportional to \( \Delta v \)).

Mission 8:
- Initial velocity: \( 4 \, \text{cm/s} \) right
- Change in velocity: Let's say force direction right, strength 4 (less than Mission 7's force? Wait, maybe Mission 7: initial 6, final 4 (change -2), Mission 8: initial 4, if force right, strength 3, change in velocity: \( 1 \, \text{cm/s} \) (so final 5, change 1). But maybe the table is to fill with assumed values to show the relationship.

But maybe the key is to observe that as force strength increases, change in velocity (magnitude) increases (if direction is same for speeding up, or opposite for slowing down). But the table is for filling. Let's fill:

Mission 6:
- Change in velocity: start (speed up from 0)
- Force direction: right
- Force strength: 3
- Change in velocity (cm/s): 2 (since 0 + 2 = 2)

Mission 7:
- Change in velocity: slow down (since initial 6, final 4)
- Force direction: left
- Force strength: 4
- Change in velocity (cm/s): -2 (4 - 6 = -2)

Mission 8:
- Change in velocity: speed up (since initial 4, final 5)
- Force direction: right
- Force strength: 2
- Change in velocity (cm/s): 1 (5 - 4 = 1)

Now, observing the relationship: The greater the force strength (in the direction of motion for speeding up, opposite for slowing down), the greater the magnitude of change in velocity (if time is constant, since \( \Delta v \propto F \) for constant mass and time).

But maybe the problem is to fill the table. Let's present the filled table (simplified):

| Mission | Initial Velocity | Change in Velocity (qualitative) | Force Direction | Force Strength | Change in Velocity (cm/s) |
|---------|------------------|----------------------------------|-----------------|----------------|---------------------------|
| 6 | 0 cm/s | Start (speed up) | Right | 3 | 2 |
| 7 | 6 cm/s right | Slow down | Left | 4 | -2 |
| 8 | 4 cm/s right | Speed up (or slow down, but let's speed up) | Right | 2 | 1 |

The relationship noticed: The strength of the force (and its direction relative to motion) affects the size of the velocity change. A stronger force (in the direction of motion) causes a larger increase in velocity; a stronger force opposite to motion causes a larger decrease (larger magnitude of change).

Answer:

The table can be filled as above, and the relationship is that force strength (and direction) determines the magnitude (and direction) of the velocity change (consistent with Newton's second law, where force is proportional to acceleration, hence to velocity change over time).