L4: UNIFORMLY ACCELERATED MOTION ALONG HORIZON

Uniformly Accelerated Motion

Motion with constant acceleration means that the velocity changes at the same rate throughout the motion.

V_f = V_i + at

use this equation when position or displacement is not mentioned in the problem

∆x = ½ (V_f + V_i)t

use this equation when acceleration is not mentioned in the problem

∆x = V_it + ½ at²

use this equation when final velocity is not mentioned in the problem

∆x = V_ft - ½ at²

Use this equation when initial velocity is not mentioned in the problem

V_f² = V_i² + 2a∆x

use this equation when time is not mentioned in the problem

Problem Solving Strategies for UAM

1. Read the problem carefully. Identify the physical quantities (time, positions, velocities, and accelerations).

2. Translate the prose into physics: “when does the particle arrive at its highest point” means “What is the value of t when x has its maximum value?”. Be alert for implicit information. For example, “A car sits at a stoplight” usually means the initial velocity is zero.

3. Write down the values of the known quantities and decide which of the unknowns are the target variables. Take note of the absence of any of the quantities that appear in the kinematic equations.

Execute the Solution

If a single equation applies, solve it for the target variable, using symbols only; then substitute the known values and calculate the value of the target variable. If you have two equations in two unknowns, solve them simultaneously for the target variables.

Evaluate your answer

Take a hard look at your results to see whether they make sense. Are they within the general range of values that you expected?