### Definition of nonuniform linear motion

Nonuniform linear motion is motion at constant acceleration. In other words, nonuniform linear motion = motion with the magnification of acceleration is constant and the direction of acceleration is constant. Direction of acceleration is constant = direction of velocity is constant = direction of displacement is constant = direction of motion is constant = the object moves in a straight line. The magnitude of constant acceleration means that the magnitude of velocity or speed increases regularly.

First example:

An object is initially at rest. One second later, the object moves at a speed of 2 m/s. Two seconds later, the object moves at a speed of 4 m/s. Three seconds later, the object moves at a speed of 6 m/s. Four seconds later, the object moves at a speed of 8 m/s. And so on…

Every 1 second, the speed of the object increases by 2 m/s. The object experience a constant acceleration of 2 m/s per 1 second or 2 m/s per second or 2 m/s^{2}.

The second example:

An object initially moves at a speed of 10 m/s. One second later.

The speed is decreased to 9 m/s. Two seconds later, the speed decreases to 8 m/s. Three seconds later, the speed is decreased to 7 m/s. Four seconds later, the speed is decreased to 6 m/s. And so on … Every 1 second, the speed of the object decreases by 1 m/s. The object has a constant deceleration of 1 m/s per 1 second or 1 m/s per second or 1 m/s^{2}.

**Equation of nonuniform linear motion**

There are three equation formulas often used:

v_{t }= v_{o} + a t

d = v_{o} t + 1⁄2 a t^{2}

v_{t}^{2 }= v_{o}^{2 }+ 2 a d

v_{o} = initial speed (meter/second), v_{t }= final speed (meter/second), a = acceleration (meter/second square), t = time interval (second), d = distance (meter).

Sample problem 1:

A particle, initially at rest, then experiences a constant acceleration of 2 m/s^{2} for 10 seconds. Calculate the final velocity of the particle.

Solution:

__Without equation:__

Acceleration (a) = 2 m/s^{2} means speed (v) increase by 2 m/s each 1 second. After 2 second, v = 4 m/s. After 10 seconds, v = 20 m/s.

__Using equation:__

__Known:__ v_{o} = 0 m/s (particle at rest), a = 2 m/s^{2}, t = 10 s

__Wanted:__ v_{t}

v_{t }= v_{o }+ a t = 0 + (2)(10) = 20 m/s

Sample problem 2:

A car moves on a straight track at a speed of 60 km/h. Because there is an obstacle, the driver brakes, so the car has a deceleration of 10 m/s2. What distance does the car still travel until it stops after braking is done?

__Known:__

v_{o }= 60 km/jam = 60(1000 m)/3600 s = 17 m/s

v_{t} = 0 m/s (car stop)

2a = – 10 m/s

__Wanted:__ distance (d)

__Solution:__

v_{t}^{2} = v_{o}^{2 }+ 2 a d

(0)^{2} = (17)^{2 }+ 2(-10) d

0 = 289 – 20 d

289 = 20 d

d = 289 : 20 = 14.45 meters

Sample problem 3:

The graph below is a nonuniform linear motion graph, v represents speed, and t states time. The magnitude of the acceleration of objects based on the graph is …

Sample problem 4:

The motion of a car produces a chart of speed (v) vs time (t) as shown in the figure on the side. If the area under the graph (shaded area) is 48 m, then the acceleration of the car is …

Shaded area = total distance = 48 meters

v_{o} = 8 m/s, v_{t} = 16 m/s, t = 1 m/s

v_{t} = v_{o} + a t

16 = 8 + a (1)

a = 16 – 8

a = 8 m/s^{2}

or

**Conceptual questions and answer about Nonuniform linear motion**

**What is nonuniform linear motion?**Nonuniform linear motion refers to the motion of an object along a straight line with a changing speed or velocity.

**How is nonuniform linear motion represented on a distance-time graph?**Nonuniform linear motion is represented by a curved line on a distance-time graph.

**What role does acceleration play in nonuniform linear motion?**Acceleration is a key factor in nonuniform linear motion. It is the rate at which velocity changes over time.

**How can one identify nonuniform linear motion on a velocity-time graph?**Nonuniform linear motion is represented by a non-horizontal (increasing or decreasing) line on a velocity-time graph, indicating that velocity changes over time.

**What is the unit of acceleration in the International System of Units (SI)?**The unit of acceleration in the SI system is meter per second squared (m/s²).

**What is the formula for displacement in nonuniform linear motion, given initial velocity, acceleration, and time?**The formula is s = ut + ½at², where s is displacement, u is initial velocity, a is acceleration, and t is time.

**Can the displacement ‘s’ be negative in nonuniform linear motion?**Yes, displacement ‘s’ can be negative in nonuniform linear motion. This would indicate motion in the opposite direction to the chosen positive direction.

**Is it possible for an object in nonuniform linear motion to come to a stop?**Yes, an object in nonuniform linear motion can come to a stop if its acceleration acts opposite to the direction of motion and sufficiently decreases the object’s velocity to zero.

**What is the formula for final velocity in nonuniform linear motion, given initial velocity, acceleration, and time?**The formula is v = u + at, where v is final velocity, u is initial velocity, a is acceleration, and t is time.

**How does the concept of jerk apply to nonuniform linear motion?**

Jerk is the rate of change of acceleration. In nonuniform linear motion, if acceleration is not constant and changes over time, then jerk is present.