While traveling south on an expressway, a car traveling 60 mph (miles per hour) slows down to 30 mph in 12 minutes due to traffic conditions. Calculate the acceleration.
Acceleration is the rate at which an object's velocity changes over time. To calculate acceleration, you need to know the initial velocity, final velocity, and the time it took for the change to occur.
In this case, the initial velocity (v₁) of the car is 60 mph, and the final velocity (v₂) is 30 mph. The time interval (Δt) in which the change occurs is given as 12 minutes.
Before we proceed, it's important to note that we need to have a consistent unit for the calculation. The time interval is given in minutes, but it's more convenient to convert it to hours to match the velocity unit. 12 minutes is equal to 12/60 = 0.2 hours.
Now, let's calculate acceleration (a) using the formula:
a = (v₂ - v₁) / Δt
Substituting the given values:
a = (30 mph - 60 mph) / 0.2 hours
Simplifying the calculation:
a = -30 mph / 0.2 hours
To simplify further, we divide both the numerator and denominator by 0.2:
a = -150 mph/h
The negative sign indicates that the car is decelerating or slowing down.
Therefore, the acceleration of the car is -150 mph/h.