If an object’s velocity increases from 13.2 m/s to 15.1 m/s in 8.0 seconds and experiences a force of 21.0 N, what is the mass of the object?

A.74 kg

B.97 kg

C.66 kg

D.88 kg


To find the mass of the object, we can use Newton's second law of motion, which states:

\[
F = ma
\]

Where:
- \( F \) is the force applied (21.0 N),
- \( m \) is the mass of the object (unknown),
- \( a \) is the acceleration of the object.

First, we need to find the acceleration. The acceleration can be calculated using the formula:

\[
a = \frac{\Delta v}{\Delta t}
\]

Where:
- \( \Delta v \) is the change in velocity,
- \( \Delta t \) is the time interval.

Given:
- Initial velocity \( v_i = 13.2 \, \text{m/s} \),
- Final velocity \( v_f = 15.1 \, \text{m/s} \),
- Time interval \( \Delta t = 8.0 \, \text{seconds} \).

The change in velocity \( \Delta v \) is:

\[
\Delta v = v_f - v_i = 15.1 - 13.2 = 1.9 \, \text{m/s}
\]

Now, calculate the acceleration:

\[
a = \frac{1.9 \, \text{m/s}}{8.0 \, \text{s}} = 0.2375 \, \text{m/s}^2
\]

Now that we have the acceleration, we can find the mass using \( F = ma \). Rearranging the equation to solve for mass \( m \):

\[
m = \frac{F}{a} = \frac{21.0 \, \text{N}}{0.2375 \, \text{m/s}^2} = 88.42 \, \text{kg}
\]

Thus, the mass of the object is approximately \( 88 \, \text{kg} \), which matches option **D**.

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Would you like further details or have any questions?

### Related Questions:
1. How would the mass change if the force applied was doubled?
2. What is the acceleration if the initial velocity was higher?
3. What is the object's velocity after 5 seconds, given the same acceleration?
4. How much force is needed to accelerate the object at twice the calculated rate?
5. What would the mass be if the time was reduced to 4 seconds?

### Tip:
Always keep track of units in calculations, especially when dealing with physical quantities like force, mass, and acceleration.

If an object’s velocity increases from 13.2 m/s to 15.1 m/s in 8.0 seconds and experiences a force of 21.0 N, what is the mass of the object?

A. 74 kg

B. 97 kg

C. 66 kg

D. 88 kg

Learn how to calculate the mass of an object given an initial velocity of 13.2 m/s, a final velocity of 15.1 m/s over 8.0 seconds, and a force of 21.0 N. This problem involves concepts from kinematics and Newton's Second Law, making it ideal for students in Grades 9-10.

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