High-performance race cars can accelerate from 0 m/s to 27 m/s (60 mi/h) in about 4 s. To see how large the acceleration due to gravity is, determine the time required for an object dropped from rest to attain a speed of 27 m/s. Ignore air resistance.
v = g t
27 = 9.8 t
t = 27/9.8 about 2.7 seconds
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To determine the time required for an object dropped from rest to attain a speed of 27 m/s, we can use the equation of motion:
\(v = u + at\)
where:
- v is the final velocity (27 m/s)
- u is the initial velocity (0 m/s)
- a is the acceleration
- t is the time
In this case, the object is dropped from rest, so the initial velocity (u) is 0 m/s, and the acceleration (a) is the acceleration due to gravity, which is approximately 9.8 m/s².
Now, we can plug in the values and solve for time (t):
\(27 = 0 + 9.8t\)
Simplifying the equation:
\(27 = 9.8t\)
Divide both sides by 9.8:
\(t = \frac{27}{9.8}\)
Calculating the value:
\(t \approx 2.755\) seconds (rounded to three decimal places)
Therefore, the time required for an object dropped from rest to attain a speed of 27 m/s is approximately 2.755 seconds.
To determine the time required for an object dropped from rest to attain a speed of 27 m/s, we need to calculate the acceleration due to gravity.
The acceleration due to gravity on Earth is approximately 9.8 m/s². Therefore, any object in free fall near the surface of the Earth will experience this acceleration.
Using this information, we can use the following kinematic equation to find the time:
v = u + at
Where:
v = final velocity (27 m/s)
u = initial velocity (0 m/s, since the object is dropped from rest)
a = acceleration due to gravity (-9.8 m/s², since it acts in the opposite direction of the motion)
t = time
Rearranging the equation to solve for time (t):
t = (v - u) / a
Plugging in the values:
t = (27 m/s - 0 m/s) / (-9.8 m/s²)
Calculating this, we get:
t ≈ -2.76 seconds
However, we must note that time cannot be negative in this context. The negative sign indicates that the acceleration due to gravity is acting in the opposite direction of motion.
To obtain the positive time, we can simply take the absolute value:
t ≈ 2.76 seconds
So, the time required for an object dropped from rest to attain a speed of 27 m/s is approximately 2.76 seconds.