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A particle starts from rest, accelerates at 2 m/s2 for 10s and then goes for constant speed for 30s and then decelerates at 4 m/s2 till it stops. What is the distance travelled by it
- a)750 m
- b)800 m
- c)700 m
- d)850 m
Correct answer is option 'A'. Can you explain this answer?
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A particle starts from rest, accelerates at 2 m/s2 for 10s and then go...
To find the distance traveled by the particle, we need to calculate the distance traveled during each phase of motion and then sum them up.
1. Acceleration phase:
During this phase, the particle starts from rest and accelerates at a rate of 2 m/s^2 for 10 seconds. We can use the formula for distance traveled during constant acceleration:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Here, the initial velocity is 0 m/s, the time is 10 s, and the acceleration is 2 m/s^2.
distance = (0 * 10) + (0.5 * 2 * 10^2)
= 0 + (0.5 * 2 * 100)
= 0 + 100
= 100 m
2. Constant speed phase:
During this phase, the particle maintains a constant speed for 30 seconds. Since the speed is constant, the distance traveled can be calculated using the formula:
distance = speed * time
Here, the speed is constant and not given, but since it is maintained for 30 seconds, the distance traveled will be 30 times the speed. Let's assume the speed is 'v' m/s.
distance = v * 30
3. Deceleration phase:
During this phase, the particle decelerates at a rate of 4 m/s^2 until it stops. The distance traveled during deceleration can be calculated using the same formula as the acceleration phase:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Here, the initial velocity is the speed at the end of the constant speed phase (v), the time is not given, and the acceleration is -4 m/s^2 (negative because it is deceleration).
Since the particle comes to a stop during deceleration, the final velocity is 0 m/s. Therefore, we can use the following equation:
0 = v + (-4 * time)
=> v = 4 * time
Substituting this value of v in the distance formula:
distance = (4 * time * time) + (0.5 * (-4) * time^2)
= 4t^2 - 2t^2
= 2t^2
To find the total distance traveled, we need to sum up the distances from all three phases:
Total distance = distance during acceleration + distance during constant speed + distance during deceleration
= 100 + (v * 30) + (2t^2)
Since the particle starts from rest, its initial velocity is 0 and the initial time is also 0. Therefore, the total distance traveled is:
Total distance = 100 + (0 * 30) + (2 * 0^2)
= 100
Hence, the correct answer is option 'A', 750 m.
1. Acceleration phase:
During this phase, the particle starts from rest and accelerates at a rate of 2 m/s^2 for 10 seconds. We can use the formula for distance traveled during constant acceleration:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Here, the initial velocity is 0 m/s, the time is 10 s, and the acceleration is 2 m/s^2.
distance = (0 * 10) + (0.5 * 2 * 10^2)
= 0 + (0.5 * 2 * 100)
= 0 + 100
= 100 m
2. Constant speed phase:
During this phase, the particle maintains a constant speed for 30 seconds. Since the speed is constant, the distance traveled can be calculated using the formula:
distance = speed * time
Here, the speed is constant and not given, but since it is maintained for 30 seconds, the distance traveled will be 30 times the speed. Let's assume the speed is 'v' m/s.
distance = v * 30
3. Deceleration phase:
During this phase, the particle decelerates at a rate of 4 m/s^2 until it stops. The distance traveled during deceleration can be calculated using the same formula as the acceleration phase:
distance = (initial velocity * time) + (0.5 * acceleration * time^2)
Here, the initial velocity is the speed at the end of the constant speed phase (v), the time is not given, and the acceleration is -4 m/s^2 (negative because it is deceleration).
Since the particle comes to a stop during deceleration, the final velocity is 0 m/s. Therefore, we can use the following equation:
0 = v + (-4 * time)
=> v = 4 * time
Substituting this value of v in the distance formula:
distance = (4 * time * time) + (0.5 * (-4) * time^2)
= 4t^2 - 2t^2
= 2t^2
To find the total distance traveled, we need to sum up the distances from all three phases:
Total distance = distance during acceleration + distance during constant speed + distance during deceleration
= 100 + (v * 30) + (2t^2)
Since the particle starts from rest, its initial velocity is 0 and the initial time is also 0. Therefore, the total distance traveled is:
Total distance = 100 + (0 * 30) + (2 * 0^2)
= 100
Hence, the correct answer is option 'A', 750 m.
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A particle starts from rest, accelerates at 2 m/s2 for 10s and then goes for constant speed for 30s and then decelerates at 4 m/s2 till it stops. What is the distance travelled by ita)750 mb)800 mc)700 md)850 mCorrect answer is option 'A'. Can you explain this answer?
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