at highway speeds, a particular automobile is capable of an acceleration of about 2.6 m/s^2. at this rate, how long does it take to accelerate from 60 km/h to 110 km/h?
we know that accelaration = change in velocity/time
here change in velocity = 110 - 60 = 50km/h
converting it into m/s = 13.89m/s..
so time required to increase the velocity = 13.89/2.6
which is 5.34seconds..
To calculate the time it takes for the automobile to accelerate from 60 km/h to 110 km/h, we can use the following formula:
\(t = \frac{v_f - v_i}{a}\)
Where:
- \(t\) is the time taken to accelerate
- \(v_f\) is the final velocity (110 km/h in this case)
- \(v_i\) is the initial velocity (60 km/h in this case)
- \(a\) is the acceleration (2.6 m/s² in this case)
First, we need to convert the velocities from km/h to m/s. Since 1 km/h is equal to 0.2778 m/s, the initial and final velocities are:
\(v_i = 60 \, \text{km/h} \times 0.2778 \, \text{m/s} = 16.67 \, \text{m/s}\)
\(v_f = 110 \, \text{km/h} \times 0.2778 \, \text{m/s} = 30.56 \, \text{m/s}\)
Now we can substitute these values along with the acceleration into the formula:
\(t = \frac{30.56 \, \text{m/s} - 16.67 \, \text{m/s}}{2.6 \, \text{m/s}^2}\)
Calculating this expression, we find:
\(t = \frac{13.89 \, \text{m/s}}{2.6 \, \text{m/s}^2} ≈ 5.34 \, \text{s}\)
Therefore, it takes approximately 5.34 seconds to accelerate from 60 km/h to 110 km/h with an acceleration of 2.6 m/s².