# Projectile Motion problems

Multiple Choice

1. A car travels 30 miles at an average speed of 60 miles per hour and then 30 miles at an average speed of 30 miles per hour. The average speed the car over the 60 miles is (A) 35 m.p.h. (B) 40 m.p.h. (C) 45 m.p.h. (D) 10 m.p.h. (E) 53 m.p.h. Answer: B.

Method:

Vavg = Δx/Δt

The average speed is the total distance traveled, divided by the total time. They give us all distances traveled is, so we just need to find the time. We find the time, by applying the average velocity formula to both parts of the journey, and solving for time. Δt1 = Δx1/ Vavg , 1 = 30/60 = 0.5 hours

Δt2 = Δx2/ Vavg , 2 = 30/30 = 1.0 hours

Vavg = Δx/Δt = (30 + 30) / (0.5 + 1.0)

Vavg = 40 mi/hr

Questions 2 – 4 relate to two particles that start at x = 0 at t = 0 and move in one dimension independently of one another. Graphs, of the velocity of each particle versus time are shown below Particle A Particle B

2. Which particle is farthest from the origin at t = 2 seconds. (A) A (B) B (C) they are in the same location at t = 2 seconds (D) They are the same distance from the origin, but in opposite directions (E) It is not possible to determine Answer: B

On a Velocity vs Time graph, the total displacement is the area underneath the curve. So when you see equal parts above and below the t-Axis, that means the object is back where it started. Particle A therefore is back at the origin, whereas Particle B has only moved in a positive direction. Hence, Particle B is not at the origin, and is further away from the origin than Particle A. 3. Which particle moves with constant non-zero acceleration? (A) A (B) B (C) both A and B (D) neither A nor B (E) It is not possible to determine Answer: D

On a Velocity vs Time graph, constant non-zero acceleration means that we should be seeing a diagonal line. Neither graph qualifies. 4. Which particle is in its initial position at t = 2 seconds? (A) A (B) B (C) both A and B (D) neither A nor B (E) It...

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