Math

Question4. A car is traveling east. The graph shows the change in the velocity of the car over time, relative to the ground.
Acceleration
During this period, what is the eastward acceleration of the car relative to the ground? A. 5 m/s25 \mathrm{~m} / \mathrm{s}^{2} B. 25 m/s225 \mathrm{~m} / \mathrm{s}^{2} C. 30 m/s230 \mathrm{~m} / \mathrm{s}^{2} D. 150 m/s2150 \mathrm{~m} / \mathrm{s}^{2}

Studdy Solution

STEP 1

What is this asking? How quickly is the car's eastward speed changing over time? Watch out! Don't mix up velocity and acceleration; acceleration is how velocity changes!

STEP 2

1. Define acceleration
2. Find the initial and final velocities
3. Find the change in time
4. Calculate the acceleration

STEP 3

Alright, so acceleration tells us how quickly something's velocity is changing.
It's all about that *change* in velocity over a *change* in time!
The formula is acceleration = (change in velocity) / (change in time).

STEP 4

Let's look at the graph!
At the beginning (t=0t = 0 seconds), the car's velocity is **0 m/s**.
This is our **initial velocity**.

STEP 5

After **6 seconds**, the car's velocity is **30 m/s**.
That's our **final velocity**!

STEP 6

The graph shows us the velocity change happened over **6 seconds**.
So our **change in time** is Δt=6\Delta t = 6 seconds.

STEP 7

Now, let's plug those values into our acceleration formula!
Remember, it's the *change* in velocity divided by the *change* in time.

STEP 8

Acceleration=Final VelocityInitial VelocityChange in Time \text{Acceleration} = \frac{\text{Final Velocity} - \text{Initial Velocity}}{\text{Change in Time}}

STEP 9

So, we have: Acceleration=30 m/s0 m/s6 s \text{Acceleration} = \frac{30 \text{ m/s} - 0 \text{ m/s}}{6 \text{ s}}

STEP 10

Acceleration=30 m/s6 s \text{Acceleration} = \frac{30 \text{ m/s}}{6 \text{ s}}

STEP 11

Acceleration=5 m/s2 \text{Acceleration} = 5 \text{ m/s}^2

STEP 12

The eastward acceleration of the car is 5 m/s25 \text{ m/s}^2, so the answer is A!

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