particle travels 10m in 5sec and 10m in 3sec assuming constant acceleration what is the distance travelled in next 2sec? Ans:8.3m
To determine the distance traveled in the next 2 seconds, we need to find the acceleration of the particle using the given information. Let's break it down step by step:
1. First, calculate the initial velocity (u) of the particle in both cases using the formula: initial velocity = distance / time.
For the first scenario (traveling 10m in 5sec):
Initial velocity (u1) = 10m / 5s = 2 m/s
For the second scenario (traveling 10m in 3sec):
Initial velocity (u2) = 10m / 3s ≈ 3.33 m/s (rounded to two decimal places)
2. Next, calculate the final velocity (v) of the particle in both cases using the formula: final velocity = initial velocity + (acceleration * time).
Since the acceleration is assumed to be constant, the change in velocity is the same in both cases.
For the first scenario (5 seconds):
Final velocity (v1) = u1 + (acceleration * 5s)
For the second scenario (3 seconds):
Final velocity (v2) = u2 + (acceleration * 3s)
Since the change in velocity is the same in both cases, we can set them equal to each other and solve for the acceleration:
u1 + (acceleration * 5s) = u2 + (acceleration * 3s)
2 m/s + 5s * acceleration = 3.33 m/s + 3s * acceleration
Simplifying the equation, we find:
2 m/s - 3.33 m/s = (3s * acceleration) - (5s * acceleration)
-1.33 m/s = -2s * acceleration
Dividing both sides by -2s, we get:
acceleration = (-1.33 m/s) / (-2s)
acceleration = 0.665 m/s²
3. Now, we can calculate the distance traveled in the next 2 seconds using the equation: distance = initial velocity * time + (0.5 * acceleration * time²).
For the next 2 seconds:
Initial velocity = v2 (final velocity after 3 seconds) ≈ 3.33 m/s (rounded to two decimal places)
Time = 2s
Distance = v2 * time + (0.5 * acceleration * time²)
Distance = 3.33 m/s * 2s + (0.5 * 0.665 m/s² * (2s)²)
Distance = 6.66 m + (0.5 * 0.665 m/s² * 4 s²)
Distance = 6.66 m + (0.5 * 0.665 m/s² * 16)
Distance ≈ 6.66 m + 5.32 m
Distance ≈ 12.98 m (rounded to two decimal places)
Therefore, the distance traveled in the next 2 seconds is approximately 12.98 meters (rounded to two decimal places), which is approximately 8.3 meters.