One Dimensional Kinematics

  1. The fastest car in the world is the Bugatti Veyron Super Sport which can reach a speed of 415 km/hr.  How long would it take you to drive across the Brooklyn Bridge (length of 1.8km) in this car at full speed?
  2. The distance from New York to Los Angeles is about 3935km. If a typical flight takes 5 hours, what is the average velocity of the jet plane?
  3.  Micheal Phelps broke his first world record in 2001, swimming the 200m butterfly in 1 minute and 55 seconds.  What was his speed in m/s?  In km/h?
  4. Usain Bolt reaches a top speed of 27.7 mph. How long would it take him to run 200m at his top speed?
  5. A cheetah can accelerate from rest to 60mph in 3 seconds. What is the cheetah’s acceleration in m/s²?
  6. If a car goes from 0 to 30mph with an acceleration of 9.8 m/s², how long is it accelerating for?
  7. A fast sport bike can accelerate at almost 10 m/s².  If a rider is traveling at 30 km/h and accelerates at this rate for 3 seconds what will their final speed be in km/h?
  8. If the position of a bowling ball is given by the formula x(t) = 5t^3 + 2 t - 80, what is the velocity of the bowling ball as a function of time? what is the acceleration of the bowling ball as a function of time?
  9. If the acceleration of  a baseball as a function of time is given by a(t) = -0.5t and it’s velocity and position at t=0 are  25m/s and 5m, what is an expression for the baseball’s velocity as a function of time? what is an expression for the baseball’s position as a function of time?
Constant Acceleration
  1. If a train is traveling at 10m/s as it enters a station and needs to stop in 100m, at what rate must it decelerate?
  2. If a car is traveling at 8 m/s and accelerates at 4m/s², how far will it travel in 8s?
  3. A plane is flying at 45m/s. It accelerates at 2m/s² until it reaches a speed of 65m/s.  How far does it travel while it accelerates?
  4. A motorcycle is 500m from the finishing line at a race and traveling at 35m/s. If the driver constantly accelerates at 1.5m/s² till she reaches the finish line how long will it take her to finish the race?
Free Fall
  1. If you drop a penny off the Empire State Building (height of 381m) how fast will it be going when it hits the sidewalk below ignoring air resistance?  Note you can’t ignore air resistance in this case, the penny reaches its  terminal velocity of about 20m/s not the velocity you get without air resistance.
  2. If you throw a baseball straight up into the air at 8m/s how long will it take to come back down to your hand? Ignore air resistance.
  3. If you want to knock an apple out of a tree 12m above you, how fast must you throw a rock in order to hit the apple? Ignore air resistance.

Two Dimensional Kinematics

  1. If a pigeon flies 25km north and then 10km to the south west and then 15km 30° north of east how far will the bird have traveled from its original location?
  2. If a plane flies 75km south, then 50km 25° north of west and then 85km in a northeast direction what will be its final displacement from its original location?
  3. If you are on an aircraft carrier traveling 5m/s to the north and an aircraft is taking off on the runway at 20m/s relative to the aircraft carrier in a southwest direction, what is the aircrafts velocity (magnitude and direction) relative to the land?
  4. If you are on a train accelerating at 3m/s² and you have a toy car that accelerates at 1.2m/s² perpendicular to the direction the train is traveling, what would be the acceleration (magnitude and direction) relative to the gorund outside the train?
Projectile Motion
  1. Evel Knievel was a stunt performer who used a motorcycle to jump over cars, busses and trucks.  On October 15th, 1975 he successfully jumped over 14 Greyhound busses, a distance of 40.5 meters.  If the ramp he used for the jump was 30° from the ground how fast would he have to be going to successfully make the jump? Ignore air resistance.
  2. On July 30th, 2016 Luke Aikins successfully jumped out of a plane at 7620m without a parachute or wingsuit.  He successfully landed in a net setup to catch him.  If the plane was traveling at 120 km/hr towards the net and he simply fell in free fall, how far before the net should he jump from the plane assuming no air resistance?
  3. If you can throw a baseball  with a speed of 20m/s and you want to get it over a 15m high fence, what is the minimum angle from the ground you need to throw it at to clear the fence? Ignore air resistance.
  4. A bullet fired from a gun typically has a speed of 150 m/s.  If one fires a gun parallel to the ground and one’s arm is 1.5m above the ground, how far will the bullet travel before it hits the ground, assuming no air resistance?
  5. In basketball the 3 point line is 7.24m from the hoop which is 3m above the ground. If a player shoots the ball from a height of 2m at an angle of 45º with what velocity must the ball be thrown to make it through the hoop?