Calculus 1 : How to find acceleration

Example Questions

Example Question #31 : How To Find Acceleration

Suppose the position function of a particle can be traced by , where  is in seconds. What is the acceleration of the particle at ?

Explanation:

To find the acceleration of the particle given the position function, take the 2nd derivative of the position function using the Power Rule.

Substitute  into the acceleration function to find the acceleration at the given time.

Example Question #32 : How To Find Acceleration

A car is driving north on a highway at a constant velocity of  mph.  What is the acceleration after an hour?

Explanation:

If a car is travelling north at constant velocity 60 mph, it's possible to write a velocity function for this vehicle, where  is time in hours.

To find the acceleration, take the derivative of the velocity function.

The acceleration after an hour, or any time , is zero.

Example Question #33 : How To Find Acceleration

The velocity of an object is given by the equation . What is the equation of acceleration of the object?

Explanation:

The acceleration of the object can be found by taking the derivative of the velocity equation.

The acceleration equation is then

Example Question #34 : How To Find Acceleration

If a car's velocity goes from  mph to  mph in  seconds, what is the average acceleration?

Explanation:

Write the formula for average acceleration.

The initial velocity is 50 mph, and the final velocity is 20 mph.

Substitute all givens and solve for the acceleration.

Example Question #35 : How To Find Acceleration

The position of an object is describe by the function .   What is the acceleration at ?

Acceleration cannot be negative.

Explanation:

To find the acceleration function, derive  twice. To do this, use the Power Rule along with the Chain Rule.

Substitute  into the acceleration function and solve.

Example Question #31 : How To Find Acceleration

Consider the position function , which describes the positon of an oxygen molecule.

Find the function which models the acceleration of the particle.

Explanation:

Recall that velocity is the first derivative of position and acceleration is the second derivative of position.

So given:

Apply the power rule to each term to find the velocity.

Applying the power rule a second time we arrive at the acceleration function.

Example Question #37 : How To Find Acceleration

Consider the position function , which describes the positon of an oxygen molecule.

Find the acceleration of the particle after  seconds.

Explanation:

Recall that velocity is the first derivative of position and acceleration is the second derivative of position.

So given:

Find a(3) to find the acceleration after 3 seconds:

So our acceleration after three seconds is 224 units per second

Example Question #38 : How To Find Acceleration

Find the acceleration of an object at  if the velocity function is .

Explanation:

To find the acceleration of an object from the velocity function, simply take the derivative of the velocity function and substitute  into the acceleration function.

Take the derivative of .

Substitute the time to find acceleration.

Example Question #39 : How To Find Acceleration

The displacement of an object at time  is defined by the function . What is the acceleration at ?

Explanation:

The acceleration is the 2nd derivative of the displacement. Knowing the equation of displacement,  we can use the power rule to differentiate.

Differentiating the equation gives us the velocity,

Differentiating the equation a second time gives us the acceleration.

Example Question #40 : How To Find Acceleration

The velocity of an object at time  is defined by the function . What is the acceleration when ?