Question
An object initially at rest falls freely near Earth's surface. How long does it take the object to attain a speed of 98 m/s?
A.
0.1 s
B.
10 s
C.
98 s
D.
960 s
A.
0.1 s
B.
10 s
C.
98 s
D.
960 s
Answers
GPT-4o mini
To determine how long it takes for an object to reach a speed of 98 m/s when falling freely under the influence of gravity, we can use the formula for uniform acceleration:
\[
v = u + at
\]
Where:
- \(v\) is the final velocity (98 m/s),
- \(u\) is the initial velocity (0 m/s, since the object starts from rest),
- \(a\) is the acceleration (approximately 9.81 m/s² due to gravity),
- \(t\) is the time in seconds.
Since the object starts from rest (\(u = 0\)), the equation simplifies to:
\[
v = at
\]
Now, we can rearrange the equation to solve for \(t\):
\[
t = \frac{v}{a}
\]
Substituting the known values:
\[
t = \frac{98 \, \text{m/s}}{9.81 \, \text{m/s}^2}
\]
Calculating this gives:
\[
t \approx 9.98 \, \text{s}
\]
So, rounding to the nearest whole number, it takes approximately 10 seconds for the object to reach a speed of 98 m/s.
Thus, the correct answer is:
**B. 10 s**
\[
v = u + at
\]
Where:
- \(v\) is the final velocity (98 m/s),
- \(u\) is the initial velocity (0 m/s, since the object starts from rest),
- \(a\) is the acceleration (approximately 9.81 m/s² due to gravity),
- \(t\) is the time in seconds.
Since the object starts from rest (\(u = 0\)), the equation simplifies to:
\[
v = at
\]
Now, we can rearrange the equation to solve for \(t\):
\[
t = \frac{v}{a}
\]
Substituting the known values:
\[
t = \frac{98 \, \text{m/s}}{9.81 \, \text{m/s}^2}
\]
Calculating this gives:
\[
t \approx 9.98 \, \text{s}
\]
So, rounding to the nearest whole number, it takes approximately 10 seconds for the object to reach a speed of 98 m/s.
Thus, the correct answer is:
**B. 10 s**