At highway speeds, a particular automobile is capable of an acceleration of about 1.6 m/s2. At this rate, how long does it take to accelerate from 81 km/h to 117 km/h?
Vo = 81000m/h * (1/3600)h/s = 22.5m/s.
Vf = 117000m/h * (1/3600)h/s = 32.5m/s.
Vf = Vo + at,
t = (Vf-Vo) / a
t = (32.5 - 22.5)/ 1.6 = 6.25s.
To find the time it takes to accelerate from 81 km/h to 117 km/h, we need to convert the velocities to meters per second and then use the formula for acceleration:
1. Convert 81 km/h to m/s:
- 1 km/h = 0.2778 m/s
- 81 km/h = 81 * 0.2778 = 22.22 m/s
2. Convert 117 km/h to m/s:
- 117 km/h = 117 * 0.2778 = 32.5 m/s
3. Calculate the change in velocity:
- Change in velocity = Final velocity - Initial velocity
- Change in velocity = 32.5 m/s - 22.22 m/s = 10.28 m/s
4. Now, use the formula for acceleration:
- Acceleration = Change in velocity / Time
We know the acceleration is 1.6 m/s^2, and we want to find the time it takes to achieve a change in velocity of 10.28 m/s. So, we rearrange the formula and solve for time:
Time = Change in velocity / Acceleration
= 10.28 m/s / 1.6 m/s^2
= 6.425 seconds
Therefore, it takes approximately 6.425 seconds to accelerate from 81 km/h to 117 km/h at a rate of 1.6 m/s^2.
To calculate the time it takes to accelerate from 81 km/h to 117 km/h, we can use the equation of motion:
\(v = u + at\)
Where:
- v = final velocity
- u = initial velocity
- a = acceleration
- t = time
First, we need to convert the velocities from km/h to m/s.
1 km/h is equivalent to 0.278 m/s.
Therefore, 81 km/h is equal to \(81 \times 0.278 = 22.518\) m/s,
and 117 km/h is equal to \(117 \times 0.278 = 32.526\) m/s.
Now, we can rearrange the equation of motion to solve for time (t):
\(t = \frac{v - u}{a}\)
Substituting the values into the equation:
\(t = \frac{32.526 - 22.518}{1.6}\)
Calculating further:
\(t = \frac{10.008}{1.6}\)
\(t = 6.255\) seconds
Therefore, it would take approximately 6.255 seconds to accelerate from 81 km/h to 117 km/h.