The position of a particle moving along x – axis in given by x = 10t – 2t². Then the time(t) at which it will momently come to rest is : (A) zero (B) 3.5s (C) 2.5s (D) 10s
1) A
2) B
3) C
4) D
Study QuestionsBegginer
The position of a particle moving along x – axis in given by x = 10t – 2t². Then the time(t) at which it will momently come to rest is : (A) zero (B) 3.5s (C) 2.5s (D) 10s
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The correct answer is C
To find the time at which the particle momentarily comes to rest, we need to determine the velocity of the particle and find the time when the velocity is zero.
Given that the position of the particle along the x-axis is given by the equation x = 10t – 2t².
To find the velocity, we differentiate the position equation with respect to time (t):
v = dx/dt = d/dt(10t – 2t²)
v = 10 – 4t
Now we can find the time at which the velocity is zero by setting v = 0 and solving for t:
10 – 4t = 0
4t = 10
t = 10/4
t = 2.5 seconds
Therefore, the time at which the particle momentarily comes to rest is 2.5 seconds.
Hence, the answer is (C) 2.5s.