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Velocity of particle depends on its position as v=x^2 +1 m/s. Find acceleration at x=1m.?
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Velocity of particle depends on its position as v=x^2 +1 m/s. Find acc...
Finding Acceleration at x=1m
- Given: Velocity function of particle is v=x^2 1 m/s
- To Find: Acceleration at x=1m
Explanation:
Acceleration is defined as the rate of change of velocity with respect to time. Mathematically, it is given by:
a = dv/dt
where a is acceleration, v is velocity, and t is time.
If we want to find the acceleration at a particular position x, we need to first find the derivative of the velocity function with respect to time. Since the velocity function is given in terms of x, we need to use the chain rule to find the derivative:
dv/dt = dv/dx * dx/dt
Here, dv/dx is the derivative of the velocity function with respect to x, which is:
dv/dx = 2x
And dx/dt is the derivative of position with respect to time, which is simply the velocity:
dx/dt = v = x^2
Substituting these values in the above equation, we get:
a = dv/dt = dv/dx * dx/dt = 2x * x^2 = 2x^3
Now we can find the acceleration at x=1m by substituting x=1 in the above equation:
a = 2(1)^3 = 2 m/s^2
Conclusion:
The acceleration of the particle at x=1m is 2 m/s^2.
Community Answer
Velocity of particle depends on its position as v=x^2 +1 m/s. Find acc...
2mls^2
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Velocity of particle depends on its position as v=x^2 +1 m/s. Find acceleration at x=1m.?
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