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1D Kinematics

If train A leaves from El Paso at high noon and train B leaves from Dallas at 1 PM, you won't know when they meet unless you master 1D kinematics. What are you waiting for?

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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