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Answer :
- Time to reach top speed (t) ≈ 1.286 s
- Distance traveled (s) ≈ 1.676 m
- The tail of the snake has not gone past the mongoose.
Solve each part of the problem step by step:
Here, it is given that:
Snake's length (L) = 3.12 m
Snake's top speed ([tex]\(v_{\text{top}}\)[/tex]) = 3.24 m/s
Snake's acceleration (a) = 2.52 m/s²
A. To find the time (t) it takes for the snake to reach its top speed, we can use the formula for acceleration:
[tex]\[v_{\text{top}} = a \cdot t.\][/tex]
Solve for t:
[tex]\[t = \dfrac{v_{\text{top}}}{a}.\][/tex]
Substitute the given values:
[tex]\[t = \dfrac{3.24 \, \text{m/s}}{2.52 \, \text{m/s}^2}.\][/tex]
[tex]\[t \approx 1.2857 \, \text{s}.\][/tex]
B. To find how far the snake travels in that time, we can use the equation of motion:
[tex]\[s = ut + \dfrac{1}{2} a t^2.\][/tex]
Since the snake starts from rest (u = 0):
[tex]\[s = \dfrac{1}{2} a t^2.\][/tex]
Substitute the calculated value of t and the given value of a:
[tex]\[s = \dfrac{1}{2} \cdot 2.52 \, \text{m/s}^2 \cdot (1.2857 \, \text{s})^2.\][/tex]
Calculate s:
[tex]\[s \approx 1.676 \, \text{m}.\][/tex]
Since the snake starts at rest and its initial position is not stated, we'll presume that it is at its nose. To attain its maximal speed, the snake's nose moves at a speed of s during the time t.
The mongoose has no chance of catching the black mamba because the snake's tail has not passed it because its length L is bigger than its length s.
Thus, Time to reach top speed is 1.286 s, distance traveled is 1.676 m, the tail of the snake has not gone past the mongoose.
For more details regarding acceleration, visit:
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Final answer:
It takes the black mamba 1.29 seconds to reach its top speed of 3.24 m/s, during which it travels a distance of 2.11 meters. Given the snake's length of 3.12 m, this means the mongoose potentially has a chance to catch the snake before its tail passes by.
Explanation:
Calculating Acceleration, Time, and Distance
To calculate the time it takes for the black mamba to reach its top speed, we use the formula final velocity (v) = initial velocity (u) + acceleration (a) × time (t). Since the snake starts from rest, u is 0, so the formula simplifies to final velocity = acceleration × time. Solving for time gives us:
time = final velocity / acceleration
time = 3.24 m/s / 2.52 m/s² = 1.29 seconds
Next, we calculate the distance traveled during this acceleration. The distance (s) can be found using the formula s = ut + (1/2)at². Since the snake is accelerating from rest, u is 0, and the formula simplifies to:
distance = (1/2) × acceleration × (time) ²
distance = (1/2) × 2.52 m/s² × (1.29 s) ² = 2.11 meters
Considering the length of the snake is 3.12 m, subtracting the distance traveled from the length:
3.12 m - 2.11 m = 1.01 meters
This means the tail has not reached the spot where its head started, so the mongoose might still have a chance to catch the black mamba.
