Worksheet titled "Displacement, Velocity & Acceleration Worksheet" featuring three physics problems related to motion, including calculating time for a bacterium to cross a Petri dish, time for a child to push a cart, and average velocity for a swimmer.

Let's solve each problem step by step from the Displacement, Velocity & Acceleration Worksheet.

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Problem 1:

What is the shortest possible time in which a bacterium could move at a speed of 3.5 mm/s across a Petri dish with a diameter of 8.4 cm?

#### Step 1: Convert units to be consistent
- Speed = 3.5 mm/s
- Diameter = 8.4 cm → convert to millimeters:
$ 8.4 \text{ cm} = 84 \text{ mm} $

#### Step 2: Use the formula for time
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
$$

$$
\text{Time} = \frac{84 \text{ mm}}{3.5 \text{ mm/s}} = 24 \text{ seconds}
$$

✔ Answer: The shortest possible time is 24 seconds.

> Note: Since the bacterium moves at constant speed and we're looking for the shortest time, it must travel directly across the diameter (straight line), so distance = diameter.

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Problem 2:

A child pushes a shopping cart at a speed of 1.5 m/s. How long would it take this child to push the cart down an aisle with a length of 9.3 m?

#### Use the same formula:
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{9.3 \text{ m}}{1.5 \text{ m/s}} = 6.2 \text{ seconds}
$$

✔ Answer: It would take 6.2 seconds.

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Problem 3:

An athlete swims from one end of a 50.0 m pool in 20.0 s and makes the return trip to the starting position in 22.0 s.

We are asked:

#### a. What is the average velocity for the first half of the swim?

- Distance = 50.0 m (one-way)
- Time = 20.0 s
- Displacement = 50.0 m (since direction matters for velocity)

$$
\text{Average velocity} = \frac{\text{Displacement}}{\text{Time}} = \frac{50.0 \text{ m}}{20.0 \text{ s}} = 2.5 \text{ m/s}
$$

✔ Answer (a): 2.5 m/s (in the direction of the swim)

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#### b. What is the average velocity for the second half of the swim?

- Return trip: 50.0 m back
- Time = 22.0 s
- Displacement = -50.0 m (opposite direction)

$$
\text{Average velocity} = \frac{-50.0 \text{ m}}{22.0 \text{ s}} \approx -2.27 \text{ m/s}
$$

✔ Answer (b): -2.27 m/s (negative sign indicates opposite direction)

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#### c. What is the average velocity for the entire swim?

- Total displacement = final position – initial position
Starts at one end, ends at same point → displacement = 0 m
- Total time = 20.0 s + 22.0 s = 42.0 s

$$
\text{Average velocity} = \frac{0 \text{ m}}{42.0 \text{ s}} = 0 \text{ m/s}
$$

✔ Answer (c): 0 m/s

> Note: Average velocity depends on displacement, not distance. Since the athlete returns to start, net displacement is zero.

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✔ Final Answers:

1. 24 seconds
2. 6.2 seconds
3.
a. 2.5 m/s
b. -2.27 m/s
c. 0 m/s

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