The velocity of train increases uniformly from 20 km/h to 60 km/h in 4 hour. The distance travelled by the train during this period is

Options

A. 160 km
B. 180 km
C. 100 km
D. 120 km

Answer

To solve the problem of finding the distance traveled by the train as its velocity increases uniformly from 20 km/h to 60 km/h over a period of 4 hours, we can follow these steps:

### Step 1: Identify the given values
- Initial velocity (u) = 20 km/h
- Final velocity (v) = 60 km/h
- Time (t) = 4 hours

### Step 2: Calculate the acceleration
We can use the formula for uniform acceleration:
\[ v = u + at \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration
- \( t \) = time

Substituting the known values:
\[ 60 = 20 + a \cdot 4 \]

### Step 3: Rearranging the equation to solve for acceleration (a)
Subtract 20 from both sides:
\[ 60 - 20 = a \cdot 4 \]
\[ 40 = a \cdot 4 \]

Now, divide both sides by 4:
\[ a = \frac{40}{4} = 10 \text{ km/h}^2 \]

### Step 4: Calculate the distance traveled (s)
We can use the formula for distance under uniform acceleration:
\[ s = ut + \frac{1}{2} a t^2 \]

Substituting the known values:
\[ s = 20 \cdot 4 + \frac{1}{2} \cdot 10 \cdot (4^2) \]

### Step 5: Simplify the equation
Calculating each term:
1. \( ut = 20 \cdot 4 = 80 \text{ km} \)
2. \( \frac{1}{2} \cdot 10 \cdot (4^2) = \frac{1}{2} \cdot 10 \cdot 16 = 80 \text{ km} \)

Now, add the two results:
\[ s = 80 + 80 = 160 \text{ km} \]

### Conclusion
The distance traveled by the train during this period is **160 km**.

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