It’s the night of the BIG homecoming dance and you just can’t wait. You think you have everything planned perfectly! On your way to the dance though there is some slow driving JERK in front of you so you slam on the gas going from 30. mi/hr to 60. mi/hr. Luckily your date brought a stop watch (the color that went best with the outfit) and told you the whole thing took place in 10s. What is your acceleration and how far did you, and your extremely well equipped date, go?
To calculate the acceleration, we can use the equation:
Acceleration (a) = (final velocity - initial velocity) / time
In this case, the initial velocity (u) is 30 mi/hr, the final velocity (v) is 60 mi/hr, and the time (t) is 10 seconds.
a = (60 mi/hr - 30 mi/hr) / 10 s
a = 30 mi/hr / 10 s
a = 3 mi/hr/s
So, the acceleration during the acceleration phase is 3 mi/hr/s.
To calculate the distance traveled during the acceleration phase, we use the equation:
Distance (s) = (initial velocity * time) + (1/2 * acceleration * time^2)
Using the values we have:
s = (30 mi/hr * 10 s) + (1/2 * 3 mi/hr/s * (10 s)^2)
s = 300 mi + (1/2 * 3 mi/hr/s * 100 s^2)
s = 300 mi + (1/2 * 3 mi/hr/s * 10,000 s)
s = 300 mi + 15,000 mi
s = 15,300 mi
So, during the acceleration phase, you and your date traveled approximately 15,300 miles.
However, please note that these calculations assume constant acceleration, which may not be accurate in real-world scenarios.