Acar moving at 50 miles per hour speeds up steadily to 70 miles per hour over a period of 30 minutes. how far did it travel during the 30-minute period of acceleration?

The car will travel 30 miles during the 30-minutes period of acceleration.

Explanation:

Given data :

Initial velocity = v₁ = 50 miles/hour

Final velocity = v₂ = 70 miles/hour

Time = t = 30 min = 0.5 hour

Using the definition of acceleration, we find the acceleration (a)

                   a = (v₂ - v₁) ÷ t

                   a = (70 - 50) ÷ 0.5

                   a = 20 ÷ 0.5

                   a = 40 miles/hour²

Using 3rd equation of motion, we find the distance travel (s)

                    2as = v₂² -  v₁²

                    2(40)s = 70² - 50²

                    80 × s = 4900 - 2500

                         s = 2400 ÷ 80

                        s = 30 miles