III.1.7. The uniformly varied rectilinear motion

The uniformly varied rectilinear motion is the motion of a mobile on a rectilinear trajectory with constant acceleration.

In uniformly accelerated rectilinear motion:

• The mobile travels longer and longer distances at equal intervals.

• The momentary acceleration is equal to the average acceleration, being constant.

• Acceleration and speed have the same direction and sense as that of motion.

🔦 Remark:

The best known example of uniformly accelerated rectilinear motion is the free fall of bodies to Earth. All bodies fall to Earth with a constant acceleration, called gravitational acceleration, g = 9,81 m/s². When the body falls free, its initial velocity is v₀ = 0 m/s.

🔓 Solved problems

1. Look carefully at the data about the girl's movement. How do we determine the type of movement?

We notice that in equal time intervals (4 s), the girl travels longer and longer distances. If we calculate the speeds on each portion, they increase. The speeds increase with equal values ​​(Δv = 1 m / s) in equal time intervals (Δt = 4 s). As the acceleration is the ratio between the variation of the speed over time, it follows that the motion is uniformly accelerated rectilinear.

2. In order to overtake, a car traveling at a speed of 54 km / h accelerates by 4 m/s². How fast is the car after 5 s ?

Solution:

• We write down the data of the problem and turn them into SI:

• We write the formula for acceleration and remove the unknown, v₂:

🔐 Homework

1. A body is allowed to fall freely from a certain height with an acceleration equal to 10 m/s². After how long does the body reach a speed of 4 m/s?