show work and dont forget units!
1 what formula is used to calculate acceleration?
2 what is the si unit of acceleration?
3 what three kinds of change in motion are called acceleration? give an example of each:
type of acceleration: a. b c
example: a. b. c
4 a horse trots around a circular track, maintaining a constant speed of 5 m/s. is the horse acceleration? explain:
5 how is it possible for a runner to be accelerating if the runner runs at a constant speed of 8 miles an hour?
6 a roller coaster car rapidly picks up speed as it rolls down a slope. as it starts down the slope, its speed is 4 m/s. but 3 seconds later, at the bottom of the slope, its speed is 22 m/s. what is its average acceleration from the top of the slope to the bottom?
7 an eagle accelerates from 15 m/s to 22 m/s in 4 seconds. what is the eagle’s average acceleration?
8 a car is creepling down a deserted highway at 1 m/s. 8 minutes later, its speed is 25 m/s. what is the car’s acceleration?
(hint. 1 minute
extra
challenge! a car advertisement states that a certain car can accelerate from rest to 90 km/h in 9 seconds. find the car’s average acceleration.
(convert the units to meters and seconds!)
(1 hour=60 minutes, 1 minute = 60 seconds, 1 km = 1000 m)

Question

Accepted Answer

### Question 1: What formula is used to calculate acceleration?
# Explanation:
## Step1: Recall acceleration definition
Acceleration is the rate of change of velocity. Velocity change is final velocity ($v_f$) minus initial velocity ($v_i$), over time ($t$).
## Step2: Write the formula
The formula for acceleration ($a$) is $a = \frac{v_f - v_i}{t}$.
# Answer: The formula to calculate acceleration is $a = \frac{v_f - v_i}{t}$ (where $a$ is acceleration, $v_f$ is final velocity, $v_i$ is initial velocity, and $t$ is time).

### Question 2: What is the SI unit of acceleration?
# Explanation:
## Step1: Recall SI units of velocity and time
Velocity has SI unit $\frac{	ext{meter}}{	ext{second}}$ (m/s), time has SI unit second (s).
## Step2: Derive acceleration unit
Acceleration is $\frac{	ext{change in velocity}}{	ext{time}}$, so unit is $\frac{	ext{m/s}}{	ext{s}} = \frac{	ext{m}}{	ext{s}^2}$.
# Answer: The SI unit of acceleration is $\frac{	ext{meters}}{	ext{second}^2}$ (or $	ext{m/s}^2$).

### Question 3: What three kinds of change in motion are called acceleration? Give an example of each.
# Brief Explanations:
Acceleration occurs with: 1) **Increasing Speed** (e.g., a car speeding up from 0 to 60 mph). 2) **Decreasing Speed** (deceleration, e.g., a car braking to stop). 3) **Changing Direction** (e.g., a car turning a corner at constant speed, as direction changes).
# Answer:
- Type A: Increasing Speed; Example a: A car accelerating from 0 to 50 m/s.
- Type B: Decreasing Speed; Example b: A car slowing down at a red light.
- Type C: Changing Direction; Example c: A car turning a circular bend.

### Question 4: A horse trots around a circular track, maintaining a constant speed of 5 m/s. Is the horse accelerating? Explain.
# Brief Explanations:
Acceleration involves change in velocity (speed or direction). The horse’s speed is constant, but its direction changes (as it moves in a circle). Since velocity is a vector (includes direction), a direction change means velocity changes, so the horse is accelerating.
# Answer: Yes, the horse is accelerating. Even though speed is constant, its direction of motion changes (moving in a circle), so velocity (a vector with speed and direction) changes. Acceleration is the rate of change of velocity, so a direction change implies acceleration.

### Question 5: How is it possible for a runner to be accelerating if the runner runs at a constant speed of 8 miles an hour?
# Brief Explanations:
Acceleration depends on velocity (speed + direction). If the runner changes direction (e.g., turns a corner, runs a curve), velocity changes (due to direction change) even if speed is constant. Thus, the runner accelerates.
# Answer: A runner can accelerate at constant speed if they change direction (e.g., running a curved path or turning). Velocity includes direction, so a direction change means velocity changes, and acceleration is the rate of velocity change.

### Question 6: A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts down the slope, its speed is 4 m/s. But 3 seconds later, at the bottom of the slope, its speed is 22 m/s. What is its average acceleration from the top of the slope to the bottom?
# Explanation:
## Step1: Identify values
$v_i = 4 \, 	ext{m/s}$, $v_f = 22 \, 	ext{m/s}$, $t = 3 \, 	ext{s}$.
## Step2: Apply acceleration formula
$a = \frac{v_f - v_i}{t} = \frac{22 - 4}{3} = \frac{18}{3} = 6 \, 	ext{m/s}^2$.
# Answer: The average acceleration is $6 \, 	ext{m/s}^2$.

### Question 7: An eagle accelerates from 15 m/s to 22 m/s in 4 seconds. What is the eagle’s average acceleration?
# Explanation:
## Step1: Identify values
$v_i = 15 \, 	ext{m/s}$, $v_f = 22 \, 	ext{m/s}$, $t = 4 \, 	ext{s}$.
## Step2: Apply formula
$a = \frac{v_f - v_i}{t} = \frac{22 - 15}{4} = \frac{7}{4} = 1.75 \, 	ext{m/s}^2$.
# Answer: The eagle’s average acceleration is $1.75 \, 	ext{m/s}^2$.

### Question 8: A car is creeping down a deserted highway at 1 m/s. 8 minutes later, its speed is 25 m/s. What is the car’s acceleration? (Hint: 1 minute = 60 seconds)
# Explanation:
## Step1: Convert time to seconds
$t = 8 \, 	ext{min} 	imes 60 \, 	ext{s/min} = 480 \, 	ext{s}$.
## Step2: Identify $v_i$, $v_f$
$v_i = 1 \, 	ext{m/s}$, $v_f = 25 \, 	ext{m/s}$.
## Step3: Apply acceleration formula
$a = \frac{v_f - v_i}{t} = \frac{25 - 1}{480} = \frac{24}{480} = 0.05 \, 	ext{m/s}^2$.
# Answer: The car’s acceleration is $0.05 \, 	ext{m/s}^2$.

### Challenge: A car advertisement states that a certain car can accelerate from rest to 90 km/h in 9 seconds. Find the car’s average acceleration. (Convert units to meters and seconds)
# Explanation:
## Step1: Convert initial velocity ($v_i$)
Rest means $v_i = 0 \, 	ext{m/s}$.
## Step2: Convert final velocity ($v_f$)
$90 \, 	ext{km/h} = 90 	imes \frac{1000 \, 	ext{m}}{3600 \, 	ext{s}} = 25 \, 	ext{m/s}$.
## Step3: Identify time ($t$)
$t = 9 \, 	ext{s}$.
## Step4: Apply acceleration formula
$a = \frac{v_f - v_i}{t} = \frac{25 - 0}{9} \approx 2.78 \, 	ext{m/s}^2$.
# Answer: The car’s average acceleration is approximately $2.78 \, 	ext{m/s}^2$ (or $\frac{25}{9} \, 	ext{m/s}^2$).

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QUESTION IMAGE

Question

Explanation:

Question 1: What formula is used to calculate acceleration?

Step1: Recall acceleration definition

Step2: Write the formula

Step1: Recall SI units of velocity and time

Step2: Derive acceleration unit

Answer:

Question 2: What is the SI unit of acceleration?