Forces and Motion

Assessment Problems

• 1. A car travels for 2 hours at 50 miles/hour and another hour at 100 miles/hour. What is the car’s average speed for the trip?

Answer: Determine how far the car traveled in each part of the trip.

(50 mi/hr) 2 hrs = 100 miles

(100 mi/hr) 1 hr = 100 miles

The total distance traveled is 200 miles.  Then v = d/t = 200 mi/3 hr = 67 mi/hr.

• 2. Car A accelerates at a rate a for a time of t seconds. Car B undergoes acceleration at a rate of 2a for a time of t/2 seconds. Which car traveled the greater distance? Assume both cars start from rest.

Answer: Car A travels twice as far as car B.  As an example, let car A accelerate at 1 m/s2 for 10 seconds.

Then dA = ½at2 = ½(1 m/s2)(10 s)2 = 50 m

The distance traveled by car B would then be dB = ½(2 m/s2)(5 s)2 = 25 m

• 3. A student throws a rock horizontally from the top of a cliff into a lake at the same instant a second student drops a rock vertically downward. If the rocks are released at the same instant and fall the same vertical height, which rock hits the water first?

Answer: Both rocks will strike the water at the same time.

The horizontal motion of the rock is independent of the vertical displacement.

• 4. How would your answer change if the initial speed of the rock thrown horizontally was doubled?

Answer: Again, both rocks will strike the water at the same time.

The rock thrown horizontally will land twice as far from the base of the cliff.