Question

Two highways meet at right angles in a town. Both highways are exactly straight

lines. Two cars leave the intersection at exactly the same time. One car starts traveling East

at 40mph and is decelerating at a rate of 1mph per hour. The other car starts traveling North

at 30mph and is accelerating at a rate of 0.5mph. At what rate is the distance between them

increasing 4 hours after they leave the intersection?

Answer 1

Explanation:

Using the relation :

S = ut + 1/2at²

S = distance

Car A :

Initial speed, u = 40 mph

a = negative acceleration = - 1 mph

At time, t = 4

S = 40(4) - 0.5(1)(4²)

S = 160 - 8

S = 152 miles

Car B :

Initial speed, u = 30 mph

a = acceleration = 0.5 mph

S = 30(4) - 0.5(1)(4²)

S = 120 - 8

S = 118 m

Change in distance / time

Rate of change = (152 - 118)m / 4 hours

Rate of change = 34 mi / 4 hr

Rate of change = 8.5 miles per hour