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a particle starts moving with acceleration 2 ms-2 distance travelled in 5th half second is 1)1.25 m2)2 .25 m3)6.25 m4)30.25 m pls give me steps
Most Upvoted Answer
a particle starts moving with acceleration 2 ms-2 distance travelled i...
Solution:
Given, acceleration of the particle = 2 m/s^2
We know that acceleration is the rate of change of velocity.
So, let's find the velocity of the particle after 5th half second.
Calculations:
In the first half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the second half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the third half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the fourth half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the fifth half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
Therefore, the distance travelled by the particle in the first 5 half seconds = 5 * (1/8) = 5/8 m
Hence, the option (1) 1.25 m is incorrect.
To find the velocity of the particle:
In the first half second, velocity (v) = u + a * t
= 0 + 2 * (1/2)
= 1 m/s
In the second half second, velocity (v) = u + a * t
= 1 + 2 * (1/2)
= 2 m/s
In the third half second, velocity (v) = u + a * t
= 2 + 2 * (1/2)
= 3 m/s
In the fourth half second, velocity (v) = u + a * t
= 3 + 2 * (1/2)
= 4 m/s
In the fifth half second, velocity (v) = u + a * t
= 4 + 2 * (1/2)
= 5 m/s
Therefore, the distance travelled by the particle in the fifth half second = (1/2) * (u + v) * t
= (1/2) * (4 + 5) * (1/2)
= 9/8 m
Hence, the option (2) 2.25 m is incorrect.
Again, the distance travelled by the particle in the first 5 half seconds = 5/8 m
So, the distance travelled by the particle in the last half second = (9/8) - (5/8) = 1/2 m
Hence, the option (3) 6.25 m is incorrect.
Final answer:
Therefore, the correct option is
Given, acceleration of the particle = 2 m/s^2
We know that acceleration is the rate of change of velocity.
So, let's find the velocity of the particle after 5th half second.
Calculations:
In the first half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the second half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the third half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the fourth half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
In the fifth half second, distance travelled (s) = (1/2) * a * t^2
= (1/2) * 2 * (1/2)^2
= 1/8 m
Therefore, the distance travelled by the particle in the first 5 half seconds = 5 * (1/8) = 5/8 m
Hence, the option (1) 1.25 m is incorrect.
To find the velocity of the particle:
In the first half second, velocity (v) = u + a * t
= 0 + 2 * (1/2)
= 1 m/s
In the second half second, velocity (v) = u + a * t
= 1 + 2 * (1/2)
= 2 m/s
In the third half second, velocity (v) = u + a * t
= 2 + 2 * (1/2)
= 3 m/s
In the fourth half second, velocity (v) = u + a * t
= 3 + 2 * (1/2)
= 4 m/s
In the fifth half second, velocity (v) = u + a * t
= 4 + 2 * (1/2)
= 5 m/s
Therefore, the distance travelled by the particle in the fifth half second = (1/2) * (u + v) * t
= (1/2) * (4 + 5) * (1/2)
= 9/8 m
Hence, the option (2) 2.25 m is incorrect.
Again, the distance travelled by the particle in the first 5 half seconds = 5/8 m
So, the distance travelled by the particle in the last half second = (9/8) - (5/8) = 1/2 m
Hence, the option (3) 6.25 m is incorrect.
Final answer:
Therefore, the correct option is
Community Answer
a particle starts moving with acceleration 2 ms-2 distance travelled i...
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a particle starts moving with acceleration 2 ms-2 distance travelled in 5th half second is 1)1.25 m2)2 .25 m3)6.25 m4)30.25 m pls give me steps
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