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Position of a particle as a function of time is given as x2 = at2 + 2bt + c, where a, b, c are constants. Acceleration of particle varies with x–n then value of n is.
Correct answer is '3'. Can you explain this answer?
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Position of a particle as a function of time is given as x2 = at2 + 2b...
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Position of a particle as a function of time is given as x2 = at2 + 2b...
To find the acceleration of the particle as a function of x, we need to differentiate the given equation twice with respect to time.
First, differentiate x^2 = at^2 + 2bt + c with respect to time:
2x(dx/dt) = 2at + 2b
Simplify to get:
dx/dt = (at + b)/x
Now differentiate again with respect to time:
(d^2x/dt^2) = a/x - [(at+b)/x]^2
Simplify further to get:
(d^2x/dt^2) = a/x - (a^2t^2 + 2abt + b^2)/x^2
Therefore, the acceleration of the particle as a function of x is given by:
a(x) = a/x - (a^2t^2 + 2abt + b^2)/x^2
Note that this expression is dependent on both x and t, as well as the constants a, b, and c.
First, differentiate x^2 = at^2 + 2bt + c with respect to time:
2x(dx/dt) = 2at + 2b
Simplify to get:
dx/dt = (at + b)/x
Now differentiate again with respect to time:
(d^2x/dt^2) = a/x - [(at+b)/x]^2
Simplify further to get:
(d^2x/dt^2) = a/x - (a^2t^2 + 2abt + b^2)/x^2
Therefore, the acceleration of the particle as a function of x is given by:
a(x) = a/x - (a^2t^2 + 2abt + b^2)/x^2
Note that this expression is dependent on both x and t, as well as the constants a, b, and c.
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Position of a particle as a function of time is given as x2 = at2 + 2b...
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Position of a particle as a function of time is given as x2 = at2 + 2bt + c, where a, b, c are constants. Acceleration of particle varies with x–n then value of n is. Correct answer is '3'. Can you explain this answer?
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