AP Calculus BC : Velocity, Speed, Acceleration
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Example Questions
Example Question #191 : Derivatives
A particle moves in space with velocity given by
where 
Find the acceleration of the particle when t=4.
To find the acceleration of the particle, we must take the first derivative of the velocity function:
The derivative was found using the following rule:
Now, we evaluate the acceleration function at the given point:
Example Question #12 : Applications Of Derivatives
Find the velocity function from an acceleration function given by
and the condition
Acceleration is the rate of change of velocity, so we must integrate the acceleration function to find the velocity function:
The integration was performed using the following rules:
To find the integration constant C, we must use the initial condition given:
Our final answer is
Example Question #13 : Applications Of Derivatives
The velocity of a particle is given by v(t). Find the function which models the particle's acceleration.
The velocity of a particle is given by v(t). Find the function which models the particle's acceleration.
To find the acceleration from a velocity function, simply take the derivative.
In this case, we are given v(t), and we need to find v'(t) because v'(t)=a(t).
To find v'(t), we need to use the power rule.
For each term, simply multiply by the exponent, and then subtract one from the exponent. Constant terms will drop out, linear terms will become constants, and so on.
So, our answer is:
Example Question #11 : Applications Of Derivatives
The velocity of a particle is given by v(t). Find the particle's acceleration when t=3.
The velocity of a particle is given by v(t). Find the particle's acceleration when t=3.
To find the acceleration from a velocity function, simply take the derivative.
In this case, we are given v(t), and we need to find v'(t) because v'(t)=a(t).
To find v'(t), we need to use the power rule.
For each term, simply multiply by the exponent, and then subtract one from the exponent. Constant terms will drop out, linear terms will become constants, and so on.
So, our acceleration function is:
Now, plug in 3 for t and solve.
So, our answer is 52.
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