What is the distance travelled by a car at a constant acceleration of 2 km/hr² when its initial velocity is 30km/hr during the time frame of Time initial = 20 seconds and Time final = 60 secnods

To find the distance traveled by the car during the specified time interval, we can use the equation for distance traveled under constant acceleration:

\[
s = v_i t + \frac{1}{2} a t^2
\]

However, since the time interval is given from \( t_1 = 20 \) seconds to \( t_2 = 60 \) seconds, we need to calculate the distance at both \( t_1 \) and \( t_2 \) and then subtract the two to find the distance traveled during this interval.

### Given:
- Initial velocity, \( v_i = 30 \) km/hr
- Acceleration, \( a = 2 \) km/hr²
- \( t_1 = 20 \) seconds
- \( t_2 = 60 \) seconds

### Step 1: Convert the times to hours
Since the velocity and acceleration are given in km/hr and km/hr², respectively, we should convert the time from seconds to hours:

\[
t_1 = \frac{20}{3600} \text{ hours} = \frac{1}{180} \text{ hours}
\]

\[
t_2 = \frac{60}{3600} \text{ hours} = \frac{1}{60} \text{ hours}
\]

### Step 2: Calculate the distance at \( t_2 \)
\[
s_2 = v_i t_2 + \frac{1}{2} a t_2^2
\]

\[
s_2 = 30 \times \frac{1}{60} + \frac{1}{2} \times 2 \times \left(\frac{1}{60}\right)^2
\]

\[
s_2 = 0.5 + \frac{1}{1800} \text{ km}
\]

\[
s_2 = 0.50056 \text{ km} 
\]

### Step 3: Calculate the distance at \( t_1 \)
\[
s_1 = v_i t_1 + \frac{1}{2} a t_1^2
\]

\[
s_1 = 30 \times \frac{1}{180} + \frac{1}{2} \times 2 \times \left(\frac{1}{180}\right)^2
\]

\[
s_1 = 0.1667 + \frac{1}{64800} \text{ km}
\]

\[
s_1 = 0.1667 \text{ km}
\]

### Step 4: Calculate the distance traveled between \( t_1 \) and \( t_2 \)
\[
\Delta s = s_2 - s_1
\]

\[
\Delta s = 0.50056 - 0.1667 = 0.33386 \text{ km}
\]

### Answer:
The distance traveled by the car between 20 seconds and 60 seconds is approximately **0.334 km**.

Would you like any further details or clarifications? Here are some related questions you might be interested in:

1. How to find the final velocity of the car after 60 seconds?
2. How does the distance traveled change if the acceleration was higher?
3. What if the initial velocity was zero instead of 30 km/hr?
4. How would the result differ if the acceleration was negative?
5. How to calculate the time taken to travel a specific distance under constant acceleration?

**Tip:** Always ensure units are consistent when applying formulas in physics or mathematics.

Learn how to calculate the distance traveled by a car with constant acceleration using the initial velocity, acceleration, and time intervals. This physics problem involves kinematics and constant acceleration formula applications. Suitable for advanced high school students.

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