91Ó°ÊÓ

In physics, constant acceleration refers to a situation where an object's acceleration does not change with time. This means that the rate at which the velocity of the object increases remains steady. If a truck, for example, starts from rest—meaning its initial speed is zero—and begins to move with a constant acceleration, its speed increases steadily each second. This constant acceleration results in a linear increase in velocity over time.

Here are some key points about constant acceleration:

• The velocity of the object increases by the same amount every second.
• The object's speed and distance traveled are predictable over time.
• Constant acceleration is common in physics problems, making it an essential concept to understand.

Understanding constant acceleration helps in solving problems involving moving objects, providing a clear framework for calculating speed and distance traveled.

Kinematics equations are a set of four equations in physics that describe the motion of objects under constant acceleration. They allow us to calculate different aspects of motion, such as speed, distance, and time.

The main kinematics equations you'll encounter are:

• \( v = u + at \)
• \( s = ut + \frac{1}{2} a t^2 \)
• \( v^2 = u^2 + 2as \)
• \( s = vt - \frac{1}{2} a t^2 \)

In these equations:

• \( v \) is the final velocity.
• \( u \) is the initial velocity.
• \( a \) is the acceleration.
• \( t \) is the time.
• \( s \) is the distance traveled.

The kinematics equations are derived from basic principles of motion and help in solving various physics problems. When you're given three known values (such as initial speed, acceleration, and time), you can use these equations to find the unknown variables.

To solve problems involving speed and distance, especially in scenarios of constant acceleration, we use specific formulas. In the given exercise, we needed to find both the speed and the distance the truck traveled.

### Calculating Speed
We used the formula \( v = u + at \). This tells us how fast the truck is moving after a certain time if it starts from a rest (zero initial speed).

The calculation involves:

• Identifying the initial speed \( u = 0 \) m/s, since the truck starts from rest.
• Using the given acceleration \( a = 5.0 \, \mathrm{m/s}^2 \).
• Multiplying the acceleration by the time \( t = 4.0 \, \mathrm{s} \).

The final speed comes out as \( v = 20 \, \mathrm{m/s} \).

### Calculating Distance
To find out how far the truck traveled, we use the formula \( s = ut + \frac{1}{2} a t^2 \). Since the initial speed is zero, it simplifies to \( s= \frac{1}{2} a t^2 \).

By substituting the known values:

• Initial speed \( u = 0 \); hence, initial distance is zero.
• The constant acceleration \( a = 5.0 \, \mathrm{m/s}^2 \).
• Squaring the time \( (4.0)^2 \).

We calculate the total distance covered as \( s = 40 \, \mathrm{m} \).

This simple exercise shows how various kinematics equations are used to solve everyday problems, elucidating distances covered and speeds achieved under constant acceleration.