# Calculus 1 : How to find acceleration

## Example Questions

### Example Question #71 : How To Find Acceleration

The position of an object is . What is the acceleration of the object?

None of the above.

Explanation:

The acceleration of the object can be found by differentiating the position equation twice, using the product rule. The product rule is where

.

Using the product rule, the velocity of the object is

.

To differentiate the velocity equation we must use the power rule and the chain rule.

The power rule is

.

The chain rule is

.

Therefore the acceleration equation is then

.

### Example Question #72 : How To Find Acceleration

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

None of these.

None of these.

Explanation:

The acceleration of the object is the derivative of the velocity. We can differentiate the velocity using the power rule where if

.

Therefore the acceleration equation of the object is

.

Because the acceleration does not have depend on the variable  the function is constant. Therefore the acceleration of the object is .

### Example Question #73 : How To Find Acceleration

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

Explanation:

The acceleration of the object can be found by differentiating the position equation of the object twice. This can be done using the power rule where if

.

Therefore the velocity equation is

.

Repeating this process gives the acceleration equation

.

Now we can find the acceleration at .

### Example Question #74 : How To Find Acceleration

The jerk of an object is given by . What is the acceleration of the object at time , if the initial acceleration of the object is ?

Explanation:

To find acceleration we integrate the jerk of the object. This can be done using the power rule where if

.

Therefore the acceleration is

.

The initial acceleration of the equation can now be used to find the value of .

Therefore  and .

The acceleration at time  can now be found.

### Example Question #75 : How To Find Acceleration

The velocity of an object is . What is the acceleration of the object at ?

Explanation:

The acceleration can be found by differentiating the velocity.

The velocity can be differentiated using the chain rule where

.

The acceleration is then

.

At , the acceleration is

.

### Example Question #76 : How To Find Acceleration

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

None of these.

Explanation:

The acceleration can be found by differentiating the position equation twice using the power rule.

The power rule is where

.

Therefore the velocity of the object is

.

The acceleration of the object can be found using the same method of differentiation as before.

Therefore the acceleration of the object is .

### Example Question #77 : How To Find Acceleration

The velocity of an object is . What is the acceleration of the object at time ?

Explanation:

The acceleration of the object is the derivative of the velocity equation. To differentiate this equation we can use the chain rule and the power rule where if

and if

.

From these rules we find that the acceleration of the object is

.

We can now find the acceleration at time  .

### Example Question #78 : How To Find Acceleration

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

Explanation:

The acceleration of the object can be found by differentiating the position twice. This can be done using the power rule where if

.

Using this we can differentiate the velocity equation.

Repeating this process we can find the acceleration equation.

We can now find the acceleration at .

### Example Question #79 : How To Find Acceleration

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

Explanation:

To find the acceleration of the object we must differentiate the position of the object twice. We can differentiate the position using the power rule and the product rule where if

and if

.

Using these rules we obtian

.

Using the same rules we can differentiate again to give the acceleration equation.

### Example Question #80 : How To Find Acceleration

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

Explanation:

The acceleration of the object can be found by differentiating the position equation twice. This can be done using the power rule where if

.

Using this rule we find that

.

Repeating this process gives us

.