Equations of Kinematics for Constant Acceleration

2.4. Equations of Kinematics for Constant Acceleration

The motion of an object traveling with constant acceleration along a straight line can be described by equations (2.4), (2.7), (2.8), and (2.9), as listed in the Quick Reference section. Note that these equations are valid only for uniform or constant acceleration. If the acceleration is changing, these equations cannot be used. One exception is if the motion can be broken up into segments in which the acceleration is constant for each segment. The kinematic equations can then be applied to each segment separately.

Example 5

Starting from rest, a car accelerates for 8.0 s to a final speed of 16 m/s. Find the acceleration of the car and the distance traveled during this time interval.

Using equation (2.4) with the initial velocity equal to zero we obtain

a = (v - v₀)/t = (16 m/s - 0 m/s)/(8.0 s) = + 2.0 m/s².

To find the distance traveled use equation (2.8)

x = v₀t + (1/2) at² = 0 + (1/2) (2.0 m/s²) (8.0 s)² = 64 m.

Note that this last result can also be obtained using equation (2.7)

x = (1/2) (v₀ + v)t = (1/2) (0 m/s + 16 m/s) (8.0 s) = 64 m.