Classical Mechanics

1D Kinematics

Position Vector for Constant Acceleration

         

If an object is thrown straight upward with an initial speed of 8 m/s8\text{ m/s} and takes 77 seconds to hit the ground, from what height was the object thrown?

Assume that gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

A race car is on a straight track. The race car accelerates from rest, covering 100 m100~\mbox{m} in 5 seconds5~\mbox{seconds}. What is the acceleration of the race car in m/s2\mbox{m/s}^2?

Details and assumptions

  • You may neglect air resistance.

A rock is dropped vertically off the edge of a cliff and hits the ground with an impact velocity of 90 m/s.90\text{ m/s}. How high is the cliff?

The gravitational acceleration is g=10 m/s2.g=10\text{ m/s}^2.

An object initially at rest starts moving in a straight line, accelerating uniformly at 3 m/s23\text{ m/s}^2 for 22 seconds. Then it moves with a constant acceleration of 2 m/s2-2\text{ m/s}^2 for 88 seconds, and then it accelerates uniformly at 1 m/s21\text{ m/s}^2 for 88 seconds. Find the displacement of the object during the total 1818 seconds.

Cliff diving is an extreme sport. If a cliff diver dives from a platform 50 meters above the water, how long does the dive take in seconds?

Details and assumptions

  • The acceleration of gravity is 9.8 m/s2-9.8~\mbox{m/s}^2.
  • The diver can be treated as a point mass and has no vertical velocity at the start of the dive.
  • Ignore air resistance.
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