Question
plane is flying at 600km/h and reduces its velocity uniformly to 70km/h in 3 mins. what is its acceleration
Answers
Answered by
GPT-4o mini
To find the acceleration of the plane, we can use the formula for acceleration, which is given by:
\[
a = \frac{\Delta v}{\Delta t}
\]
where:
- \( a \) is the acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.
1. **Convert the time from minutes to hours:**
\( 3 \) minutes = \( \frac{3}{60} \) hours = \( 0.05 \) hours
2. **Initial velocity (\( v_i \)):**
\( 600 \) km/h
3. **Final velocity (\( v_f \)):**
\( 70 \) km/h
4. **Calculate the change in velocity (\( \Delta v \)):**
\[
\Delta v = v_f - v_i = 70 \, \text{km/h} - 600 \, \text{km/h} = -530 \, \text{km/h}
\]
5. **Calculate the acceleration (\( a \)):**
\[
a = \frac{\Delta v}{\Delta t} = \frac{-530 \, \text{km/h}}{0.05 \, \text{h}} = -10600 \, \text{km/h}^2
\]
So, the acceleration of the plane is \(-10600 \, \text{km/h}^2\). This negative sign indicates a reduction in speed, confirming that it is deceleration.
\[
a = \frac{\Delta v}{\Delta t}
\]
where:
- \( a \) is the acceleration,
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the change in time.
1. **Convert the time from minutes to hours:**
\( 3 \) minutes = \( \frac{3}{60} \) hours = \( 0.05 \) hours
2. **Initial velocity (\( v_i \)):**
\( 600 \) km/h
3. **Final velocity (\( v_f \)):**
\( 70 \) km/h
4. **Calculate the change in velocity (\( \Delta v \)):**
\[
\Delta v = v_f - v_i = 70 \, \text{km/h} - 600 \, \text{km/h} = -530 \, \text{km/h}
\]
5. **Calculate the acceleration (\( a \)):**
\[
a = \frac{\Delta v}{\Delta t} = \frac{-530 \, \text{km/h}}{0.05 \, \text{h}} = -10600 \, \text{km/h}^2
\]
So, the acceleration of the plane is \(-10600 \, \text{km/h}^2\). This negative sign indicates a reduction in speed, confirming that it is deceleration.