The engineer must communicate to her crew the magnitude of the train's acceleration. The train commenced from a stationary position at the station and underwent uniform acceleration for 180 seconds until it reached its peak speed of 144 kilometers per hour. What information should the engineer convey to the crew?(1 point)

Question

Responses

The magnitude of acceleration was 0.22 m/s2.
The magnitude of acceleration was 0.22 m/s 2 .

The magnitude of acceleration was 7.2 m/s2.
The magnitude of acceleration was 7.2 m/s 2 .

The magnitude of acceleration was 0.80 m/s2.
The magnitude of acceleration was 0.80 m/s 2 .

The magnitude of acceleration was 4.5 m/s2.

Answer 1

To find the magnitude of the train's acceleration, we can use the formula:

\[ a = \frac{\Delta v}{\Delta t} \]

Where:

• \( a \) is the acceleration,
• \( \Delta v \) is the change in velocity,
• \( \Delta t \) is the change in time.

1. Convert the final speed from kilometers per hour to meters per second.
   • The final speed is 144 kilometers per hour.
   • To convert to meters per second, use the conversion factor \( \frac{1000 , \text{meters}}{1 , \text{kilometer}} \) and \( \frac{1 , \text{hour}}{3600 , \text{seconds}} \):

\[ 144 , \text{km/h} = 144 \times \frac{1000}{3600} \approx 40 , \text{m/s} \]

2. Calculate the change in velocity.

   • The train started from rest, so \( \Delta v = 40 , \text{m/s} - 0 , \text{m/s} = 40 , \text{m/s} \).

3. The time taken for the acceleration was 180 seconds.

4. Substituting into the acceleration formula:

\[ a = \frac{40 , \text{m/s}}{180 , \text{s}} \approx 0.222 , \text{m/s}^2 \approx 0.22 , \text{m/s}^2 \]

Therefore, the information the engineer should convey to the crew is:

The magnitude of acceleration was 0.22 m/s².