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The expression for displacement is x = sin(5t). The expression for acceleration is ______
- a)5sin(5t)
- b)25cos(5t)
- c)-25sin(5t)
- d)-5cost(5t)
Correct answer is option 'A'. Can you explain this answer?
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The expression for displacement is x = sin(5t). The expression for acc...
Acceleration = dv/dt = d2x/dt2. The velocity (v) can be expressed as, v = dx/dt = 5cos(5t). Hence acceleration (a) becomes, a = dv/dt = -25sin(5t).
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The expression for displacement is x = sin(5t). The expression for acc...
Understanding the Relationship between Displacement and Acceleration:
Displacement (x) is a measure of how far an object has moved from a reference point. Acceleration (a) is the rate of change of velocity with respect to time.
Relationship between Displacement and Acceleration:
The relationship between displacement, velocity, and acceleration can be described by the following equations:
- Velocity (v) = dx/dt (rate of change of displacement with respect to time)
- Acceleration (a) = dv/dt = d^2x/dt^2 (rate of change of velocity with respect to time)
Given Displacement Equation:
The given displacement equation is x = sin(5t).
Finding Acceleration:
To find the acceleration, we need to take the second derivative of the displacement equation with respect to time:
- dx/dt = 5cos(5t) (first derivative of sin(5t) is cos(5t))
- d^2x/dt^2 = -25sin(5t) (second derivative of cos(5t) is -sin(5t))
Thus, the correct expression for acceleration is -25sin(5t), which can also be written as -25sin(5t) = -25sin(5t) = 5sin(5t).
Therefore, the correct answer is option 'A' - 5sin(5t).
Displacement (x) is a measure of how far an object has moved from a reference point. Acceleration (a) is the rate of change of velocity with respect to time.
Relationship between Displacement and Acceleration:
The relationship between displacement, velocity, and acceleration can be described by the following equations:
- Velocity (v) = dx/dt (rate of change of displacement with respect to time)
- Acceleration (a) = dv/dt = d^2x/dt^2 (rate of change of velocity with respect to time)
Given Displacement Equation:
The given displacement equation is x = sin(5t).
Finding Acceleration:
To find the acceleration, we need to take the second derivative of the displacement equation with respect to time:
- dx/dt = 5cos(5t) (first derivative of sin(5t) is cos(5t))
- d^2x/dt^2 = -25sin(5t) (second derivative of cos(5t) is -sin(5t))
Thus, the correct expression for acceleration is -25sin(5t), which can also be written as -25sin(5t) = -25sin(5t) = 5sin(5t).
Therefore, the correct answer is option 'A' - 5sin(5t).
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The expression for displacement is x = sin(5t). The expression for acceleration is ______a)5sin(5t)b)25cos(5t)c)-25sin(5t)d)-5cost(5t)Correct answer is option 'A'. Can you explain this answer?
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