A certain car is capable of accelerating at a rate of +0.90 m/s2. How long does it take for this car to go from a speed of 50 mi/h to a speed of 65 mi/h?
Use the formula (change in V) = a t
But first you must convert the mi/h (mph) speeds to consistent metric units of m/s.
The 15 mph speed change corresponds to 22 ft/s or 6.71 m/s
(I have always found it convenient to remember that 15 mph is 22 ft/s, and 1 ft/s = 0.3048 m/s, exactly)
Time required = (6.71 m/s)/(0.90 m/s^2) = 7.45 seconds
To find the time it takes for the car to go from 50 mi/h to 65 mi/h, we first need to convert the speeds from miles per hour to meters per second.
1 mile is equal to 1609.34 meters, and 1 hour is equal to 3600 seconds. So, 50 mi/h is equal to (50 * 1609.34) / 3600 m/s, which is approximately 22.35 m/s. Similarly, 65 mi/h is equal to (65 * 1609.34) / 3600 m/s, which is approximately 29.05 m/s.
Now, we can use the formula for uniform acceleration to find the time it takes for the car to accelerate from 22.35 m/s to 29.05 m/s. The formula is:
v = u + at
where:
v = final velocity
u = initial velocity
a = acceleration
t = time
In this case, the initial velocity (u) is 22.35 m/s, the final velocity (v) is 29.05 m/s, and the acceleration (a) is +0.90 m/s^2. We want to find the time (t), so we rearrange the formula to solve for t:
t = (v - u) / a
Substituting the given values, we have:
t = (29.05 - 22.35) / 0.90
Calculating this, we find that the time it takes for the car to go from a speed of 50 mi/h to a speed of 65 mi/h is approximately 7.44 seconds.