A particle travels 10m in 5sec and 10m in 3sec assuming constant acceleration what is the distance travelled in next 2sec? Ans:8.3m

To find the distance traveled in the next 2 seconds, we need to first determine the acceleration of the particle.

Let's consider the first interval of time, where the particle travels 10m in 5 seconds. We can use the formula for average velocity:

Average Velocity = (Final Position - Initial Position) / Time

In this case, the initial position is 0m (assuming the particle starts from rest), the final position is 10m, and the time is 5 seconds.

So, Average Velocity = (10m - 0m) / 5s = 2m/s

Next, we consider the second interval of time, where the particle travels 10m in 3 seconds. Again, using the average velocity formula:

Average Velocity = (Final Position - Initial Position) / Time

In this case, the initial position is 10m (the final position from the previous interval), the final position is 20m, and the time is 3 seconds.

So, Average Velocity = (20m - 10m) / 3s = 10/3 m/s ≈ 3.33 m/s

Now, we can find the acceleration by subtracting the initial velocity from the final velocity and dividing it by the time taken:

Acceleration = (Final Velocity - Initial Velocity) / Time

Here, the initial velocity is 2 m/s (from the first interval) and the final velocity is 3.33 m/s (from the second interval). The time taken is the difference between the two intervals: 3s - 5s = -2s.

So, the acceleration = (3.33 m/s - 2 m/s) / -2s = 1.33 m/s^2

Now that we have the acceleration, we can find the distance traveled in the next 2 seconds using the equation of motion:

Distance = Initial Position + (Initial Velocity * Time) + (1/2 * Acceleration * Time^2)

In this case, the initial position is 20m (the final position from the second interval), the initial velocity is 3.33 m/s, the time is 2 seconds, and the acceleration is 1.33 m/s^2.
Plugging these values into the equation:

Distance = 20m + (3.33 m/s * 2s) + (1/2 * 1.33 m/s^2 * (2s)^2)
= 20m + 6.66 m + 2.66 m
= 29.32 m

So, the distance traveled in the next 2 seconds is approximately 29.32 m.

However, the given answer is 8.3m, which seems incorrect based on the information provided.