Answer :
Let's solve the problem step-by-step:
### Step 1: Identify the given values
- Final speed ([tex]\( v \)[/tex]) of the train: [tex]\( 40 \, \text{km/hr} \)[/tex]
- Time ([tex]\( t \)[/tex]) taken to reach this speed: [tex]\( 10 \, \text{minutes} \)[/tex]
### Step 2: Convert all units to be consistent
The time is given in minutes, but the speed is in kilometers per hour. To ensure consistency, we convert the time from minutes to hours.
[tex]\[ t = \frac{10 \, \text{minutes}}{60} = \frac{1}{6} \, \text{hours} \][/tex]
### Step 3: Identify the initial conditions
The train starts from rest, so the initial speed ([tex]\( u \)[/tex]) is [tex]\( 0 \, \text{km/hr} \)[/tex].
### Step 4: Calculate the acceleration
To find the acceleration ([tex]\( a \)[/tex]), we use the formula for uniform acceleration:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Substituting the known values ([tex]\( v = 40 \, \text{km/hr} \)[/tex], [tex]\( u = 0 \, \text{km/hr} \)[/tex], and [tex]\( t = \frac{1}{6} \, \text{hours} \)[/tex]) into the formula:
[tex]\[ a = \frac{40 \, \text{km/hr} - 0 \, \text{km/hr}}{\frac{1}{6} \, \text{hours}} \][/tex]
### Step 5: Simplify the expression
[tex]\[ a = \frac{40 \, \text{km/hr}}{\frac{1}{6} \, \text{hours}} = 40 \, \text{km/hr} \times 6 = 240 \, \text{km/hr}^2 \][/tex]
### Step 6: State the final result
The acceleration of the train is [tex]\( 240 \, \text{km/hr}^2 \)[/tex].
Thus, the train's acceleration is [tex]\( 240 \, \text{km/hr}^2 \)[/tex].
### Step 1: Identify the given values
- Final speed ([tex]\( v \)[/tex]) of the train: [tex]\( 40 \, \text{km/hr} \)[/tex]
- Time ([tex]\( t \)[/tex]) taken to reach this speed: [tex]\( 10 \, \text{minutes} \)[/tex]
### Step 2: Convert all units to be consistent
The time is given in minutes, but the speed is in kilometers per hour. To ensure consistency, we convert the time from minutes to hours.
[tex]\[ t = \frac{10 \, \text{minutes}}{60} = \frac{1}{6} \, \text{hours} \][/tex]
### Step 3: Identify the initial conditions
The train starts from rest, so the initial speed ([tex]\( u \)[/tex]) is [tex]\( 0 \, \text{km/hr} \)[/tex].
### Step 4: Calculate the acceleration
To find the acceleration ([tex]\( a \)[/tex]), we use the formula for uniform acceleration:
[tex]\[ a = \frac{v - u}{t} \][/tex]
Substituting the known values ([tex]\( v = 40 \, \text{km/hr} \)[/tex], [tex]\( u = 0 \, \text{km/hr} \)[/tex], and [tex]\( t = \frac{1}{6} \, \text{hours} \)[/tex]) into the formula:
[tex]\[ a = \frac{40 \, \text{km/hr} - 0 \, \text{km/hr}}{\frac{1}{6} \, \text{hours}} \][/tex]
### Step 5: Simplify the expression
[tex]\[ a = \frac{40 \, \text{km/hr}}{\frac{1}{6} \, \text{hours}} = 40 \, \text{km/hr} \times 6 = 240 \, \text{km/hr}^2 \][/tex]
### Step 6: State the final result
The acceleration of the train is [tex]\( 240 \, \text{km/hr}^2 \)[/tex].
Thus, the train's acceleration is [tex]\( 240 \, \text{km/hr}^2 \)[/tex].
