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Velocity, acceleration and distance. This equation applies to objects in uniform acceleration: (final velocity) 2 - (initial velocity) 2 = 2 × acceleration × distance. \ (v^2 - u^2 = 2~a~s ...
If any three of the five quantities are known, then the other two may be calculated using the following four equations: v = u + at. x = ut + ½at 2. x = (u+v) ÷ 2 × t. v 2 = u 2 + 2as. The...
Oct 13, 2023 · Calculate final velocity as a function of initial velocity, acceleration and displacement using v^2 = u^2 + 2as. Solve for v, u, a or s; final velocity, initial velocity, acceleration ar displacement.
There were a significant proportion of candidates who proceeded to integrate u(u + 1)–2 with respect to x and did so by either treating the leading u as a constant or using integration by parts. Many candidates correctly changed the limits from 0 and 1 to 1 and 2 to obtain their final answer.
- Kinematics Equations of Motion
- How to Select Which Equation of Motion to use?
- Derivation of Equations of Motion
- Worked Examples
The equations we’re discussing are fundamental to understanding motion, specifically when dealing with constant or uniform acceleration. Known as the equations of motion, they form the cornerstone of kinematics, a branch of classical mechanics that describes the motion of points, bodies (objects), and systems of bodies without considering the force...
You select the equations based on the amount of information that you have. If you prefer to read words, the information in the table can be found (in words) below. The above equation is suitable to use if you do not have the displacement. The above equation is suitable to use if you do not have the final velocity. The above equation is suitable to ...
Equation 1 –
Remember that equation for acceleration is the following: You can re-arrange the equation to give:
Equation 2 –
The velocity of a body moving with uniform acceleration increases steadily. Its average velocity therefore equals half the sum of its initial and final velocities: If is the distance moved in time , then since , which re-arranges to give:
Equation 3 –
Substitute the first equation into the second equation. You will get the following:
Example 1
A boy throws a ball vertically upwards. The ball falls back into his hand 2.0 seconds later. Neglecting air resistance, what is the speed at which the ball leaves his hand?
Example 2: The Racing Car
Question: A racing car accelerates from rest at a uniform acceleration of for seconds. How far does the car travel in this time?
Example 3: The Leap of Faith
Question: A stuntman jumps off a moving motorcycle to land on a moving train. The motorcycle is traveling at , and the train is accelerating away at . If the motorcycle and the train are apart when the stuntman jumps, how long does he have before the train is too far away? Assume the stuntman lands with the same speed as his jump.
A Boeing 747 lands with a velocity of 180 ms-1 and decelerates at 6 ms 2 coming to a halt in 30 seconds. Calculate the distance it took for the aircraft to come to a halt.
For an object that has an initial velocity u and that is moving in a straight line with constant acceleration a, the following equations connect the final velocity v and displacement s in a given time t. Note: These equations cannot be used if the acceleration is not constant.
