Classical Mechanics

1D Kinematics

Position Vector for Constant Acceleration


If an object is thrown straight upward with an initial speed of \(8\text{ m/s}\) and takes \(7\) seconds to hit the ground, from what height was the object thrown?

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

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

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 \(90\text{ m/s}.\) How high is the cliff?

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

An object initially at rest starts moving in a straight line, accelerating uniformly at \(3\text{ m/s}^2\) for \(2\) seconds. Then it moves with a constant acceleration of \(-2\text{ m/s}^2\) for \(8\) seconds, and then it accelerates uniformly at \(1\text{ m/s}^2\) for \(8\) seconds. Find the displacement of the object during the total \(18\) 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 \(-9.8~\mbox{m/s}^2\).
  • 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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