Practice
Motion with constant acceleration
Average velocity and acceleration, then the three constant-acceleration equations: final speed, displacement, stopping distance and free fall.
The skill
Reach for the kinematic equations when the acceleration is constant and the motion is along one line. List what you know (, , , , ), name what you want, and pick the equation that leaves out the one quantity you were not given and do not need. Choose a positive direction before writing any numbers. The most common mistake is giving a slowing object an acceleration with the same sign as its velocity: when velocity and acceleration point opposite ways, they have opposite signs.
A worked example
A car traveling at 14 m/s brakes with a constant acceleration of magnitude 6.3 m/s² until it stops.
How far does it travel while braking, in meters? Give your answer to three significant figures.
Solution
- No time is given, so use .
- Take the direction of travel as positive, so a_x = −6.3 m/s², and the final velocity is 0: 0 = 14² + 2(−6.3)(x − x₀).
- x − x₀ = 196 ÷ 12.6 = 15.6 m.
Answer: 15.6