A car 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