The kinematic equations describe motion in a straight line when acceleration is constant. They connect position, displacement, velocity, acceleration, and time, which makes them a core tool for solving many physics problems. They are often called the SUVAT equations because they use displacement s, initial velocity u, final velocity v, acceleration a, and time t.
These equations matter because they let you predict motion without needing to analyze every instant separately.
Each equation is useful when one variable is missing from the problem. For example, v = u + at is best when displacement is not needed, while v^2 = u^2 + 2as is best when time is not given. The equations apply to objects such as cars speeding up, balls falling vertically, and carts moving along tracks, as long as acceleration stays constant.
Choosing a positive direction and keeping signs consistent are just as important as substituting numbers.
Key Facts
- v = u + at relates final velocity, initial velocity, acceleration, and time.
- s = ut + 1/2 at^2 gives displacement when initial velocity, acceleration, and time are known.
- s = 1/2(u + v)t gives displacement using average velocity when acceleration is constant.
- v^2 = u^2 + 2as relates velocities, acceleration, and displacement without using time.
- For constant acceleration, average velocity is v_avg = (u + v)/2.
- Use consistent units: displacement in meters, time in seconds, velocity in m/s, and acceleration in m/s^2.
Vocabulary
- Displacement
- Displacement is the change in position of an object, including direction.
- Initial velocity
- Initial velocity is the velocity of an object at the start of the time interval being studied.
- Final velocity
- Final velocity is the velocity of an object at the end of the time interval being studied.
- Acceleration
- Acceleration is the rate at which velocity changes with time.
- Constant acceleration
- Constant acceleration means the velocity changes by equal amounts during equal time intervals.
Common Mistakes to Avoid
- Using the equations when acceleration is not constant is wrong because SUVAT equations assume a single constant value of a throughout the motion.
- Mixing up distance and displacement is wrong because displacement includes direction and can be positive or negative depending on the chosen axis.
- Forgetting the sign of acceleration is wrong because slowing down or motion in the negative direction may require a negative value for a or v.
- Choosing an equation before identifying known and unknown variables is wrong because the best equation is the one that avoids the missing variable.
Practice Questions
- 1 A car starts from rest and accelerates at 3.0 m/s^2 for 8.0 s. Find its final velocity and displacement.
- 2 A ball is thrown straight upward with an initial velocity of 20 m/s. Using a = -9.8 m/s^2, find its velocity after 1.5 s and its displacement from the release point.
- 3 A cyclist moves forward while slowing down at a constant rate. Explain how the signs of velocity and acceleration should be chosen if forward is the positive direction.