🔖 Topics

  • Position vs. Time Graphs
  • Velocity vs. Time Graphs
  • Acceleration vs. Time Graphs
  • Newton's Second Law

🎯 Objectives

  • Draw position, velocity, and acceleration vs. time graphs for a variety of physical situations
  • Use position, velocity, acceleration, time, and initial conditions to fully analyze the motion of a system
  • Apply Newton's Second Law to free body diagrams in order to calculate the acceleration of the body

📋 Sequence

  • Definitions:
    • Position vs. Displacement
    • Speed vs. Velocity
    • Instantaneous Speed/Velocity vs. Average Speed/Velocity
    • Instantaneous Acceleration vs. Average Acceleration
  • Work Through Graph Problems
  • Work Through Newton’s Second Law Problems

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

A Car Accelerating on a Flat Road: A car starts from rest on a long length of straight road. It accelerates at 10 \(m/s^2\) for 5 seconds and then continues to cruise down the road at constant velocity.

  • Draw the position vs. time graph for the car between zero and ten seconds.
  • Draw the velocity vs. time graph for the car between zero and ten seconds.
  • Draw the acceleration vs. time graph for the car between zero and ten seconds.
  • What is the instantaneous velocity at t = 5 seconds?
  • What is the average velocity over the ten second period?

A Car Braking on a Flat Road: A car with a mass of 500 kg is traveling at a constant speed of 20 m/s on long length of straight road. Seeing an obstacle ahead, the driver brakes suddenly, slowing down at a rate of 10 \(m/s^2\) until they come to a complete stop.

  • Draw the position vs. time graph for the car.
  • Draw the velocity vs. time graph for the car.
  • Draw the acceleration vs. time graph for the car.
  • What is the angle between the velocity vector and the acceleration vector of the car as it slows down?

A Ball Thrown Up Into the Air: A child throws a ball straight up into the air with an initial speed of 5 m/s.

  • Draw the position vs. time graph for the ball.
  • Draw the velocity vs. time graph for the ball.
  • Draw the acceleration vs. time graph for the ball.
  • What is the equation of the line for the velocity vs. time graph in slope-intercept form?
  • How long after the child throws the ball does it reach its maximum height?

F1 Car: F1 cars use a combination of powerful engines and aerodynamic design to maneuver effectively. A modern F1 car can go from zero to 100 km/hr in about 2.6 seconds and from 100 km/hr to 200 km/hr in about 1.9 seconds. They can decelerate from 200 km/hr back to zero in around 3 seconds. Suppose a driver starts an F1 car at rest and accelerates at full throttle until they reach 200 km/hr. They cruise at this velocity for 5 seconds before slamming the breaks and coming to a full stop.

  • Draw the position vs. time graph for the car.
  • Draw the velocity vs. time graph for the car.
  • Draw the acceleration vs. time graph for the car.
  • What is the G force on the driver during the initial acceleration from 0 - 100 km/hr?
  • What is the G force on the driver during the acceleration from 100 - 200 km/hr?
  • What is the G force on the driver while braking from 200 km/hr to a full stop? Hint: The G force the amount of acceleration a body feels in terms of the acceleration due to gravity near the surface of the Earth. GForce = Acceleration / g

Pulling a Suitcase (Revisited): You are pulling a suitcase with a mass of 15 kg through the airport at a constant acceleration by exerting a force of 50.0 N at an angle of \(45^\circ\) from the vertical. The kinetic coefficient of friction between the suitcase and the floor is 0.15. What is the acceleration of the suitcase?

Pushing a Crate (Revisited): A crate with a mass of 30 kg is sitting on the floor of a warehouse. The coefficient of kinetic friction between the crate and the floor is \(\mu_k = 0.3\).

  • Suppose I apply a horizontal force \(\vec{F} = 150 N\) to the crate so that it moves at a constant acceleration. What is the magnitude of the acceleration of the crate?
  • Suppose I apply a force \(\vec{F} = 150 N\) at \(30^\circ\) above the horizontal to the crate so that it moves at a constant acceleration. What is the magnitude of the acceleration of the crate?
  • Suppose I apply a force \(\vec{F} = 150 N\) at \(30^\circ\) below the horizontal to the crate so that it moves at a constant velocity. What is the magnitude of the acceleration of the crate?

Standing on a Scale: A 60 kg person stands on a bathroom scale in an elevator.

  • What will the weight on the scale read when the elevator is standing still?
  • What will the weight on the scale read when the elevator is moving upwards with a velocity of 10 m/s?
  • What will the weight on the scale read when the elevator is moving upwards with an acceleration of 5 \(m/s^2\)?
  • What will the weight on the scale read when the elevator is moving downwards with a velocity of 10 m/s?
  • What will the weight on the scale read when the elevator is moving downwards with an acceleration of 5 \(m/s^2\)?

✅ Partial Solutions

N/A

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.