At high speeds, a particular automobile is capable of an acceleration of about 0.510 m/s^2. At this rate, how long (in seconds) does it take to accelerate from 95.0 km/hr to 101 km/hr?
To find the time it takes for the automobile to accelerate from 95.0 km/hr to 101 km/hr, we first need to convert these speeds to meters per second (m/s), as the acceleration is given in m/s^2.
Converting 95.0 km/hr to m/s:
1 km/hr = (1000 m/3600 s) m/s (converting km/hr to m/s)
95.0 km/hr = (95.0 * (1000 m/3600 s)) m/s
= (95000/3600) m/s
= 26.39 m/s (rounded to two decimal places)
Converting 101 km/hr to m/s:
101 km/hr = (101 * (1000 m/3600 s)) m/s
= (101000/3600) m/s
= 28.06 m/s (rounded to two decimal places)
Now we have the initial velocity (u) as 26.39 m/s and the final velocity (v) as 28.06 m/s. The acceleration (a) is given as 0.510 m/s^2.
The formula to compute the time (t) it takes to accelerate from one velocity to another using constant acceleration is:
v = u + at
Rearranging the formula to solve for time (t):
t = (v - u) / a
Substituting the values into the formula:
t = (28.06 m/s - 26.39 m/s) / 0.510 m/s^2
t = 1.67 m/s / 0.510 m/s^2
t = 3.27 seconds (rounded to two decimal places)
Therefore, it takes approximately 3.27 seconds for the automobile to accelerate from 95.0 km/hr to 101 km/hr.