formulas. $$ \begin{array}{l} ext { a. } v=u+a t \ ext { - Workspace } \ ext { + Check answer }\end{array} $$

Question

formulas. $$ \begin{array}{l}	ext { a. } v=u+a t \ 	ext { - Workspace } \ 	ext { + Check answer }\end{array} $$

UpStudy AI · Accepted Answer

Certainly! Let's break down the formula you've provided:

### a. $$ v = u + a t $$

This equation is one of the fundamental kinematic equations used in physics to describe the motion of objects under constant acceleration. Here's what each symbol represents:

- **$$ v $$**: **Final Velocity**
  - The velocity of the object after time $$ t $$.

- **$$ u $$**: **Initial Velocity**
  - The velocity of the object before the time $$ t $$ has passed.

- **$$ a $$**: **Acceleration**
  - The rate at which the velocity of the object is increasing or decreasing. It's assumed to be constant in this equation.

- **$$ t $$**: **Time**
  - The duration over which the acceleration is applied.

### **Understanding the Equation**

The equation $$ v = u + a t $$ tells us how the velocity of an object changes over time when it is subjected to constant acceleration. Here's a step-by-step interpretation:

1. **Starting Point ($$ u $$)**:
   - The object begins with an initial velocity $$ u $$.

2. **Acceleration ($$ a $$)**:
   - The object experiences a constant acceleration $$ a $$. This could be speeding up ($$ a > 0 $$) or slowing down ($$ a < 0 $$, often referred to as deceleration).

3. **Time ($$ t $$)**:
   - The acceleration occurs over a period of time $$ t $$.

4. **Final Velocity ($$ v $$)**:
   - After time $$ t $$, the object's velocity changes to $$ v $$.

**Example Problem:**

*An car starts from rest ($$ u = 0 $$) and accelerates uniformly at $$ 3 \, \text{m/s}^2 $$ for $$ 5 $$ seconds. What is its final velocity?*

**Solution:**

Using the formula:
$$
v = u + a t
$$
Plug in the known values:
$$
v = 0 + (3 \, \text{m/s}^2)(5 \, \text{s}) = 15 \, \text{m/s}
$$
So, the final velocity $$ v $$ is $$ 15 \, \text{m/s} $$.

### **Additional Kinematic Equations**

While $$ v = u + a t $$ is essential, there are other kinematic equations that are frequently used:

1. **Displacement ($$ s $$) with initial velocity:**
   $$
   s = u t + \frac{1}{2} a t^2
   $$

2. **Final velocity squared:**
   $$
   v^2 = u^2 + 2 a s
   $$

3. **Displacement ($$ s $$) with average velocity:**
   $$
   s = \frac{(u + v)}{2} \times t
   $$

4. **Displacement when time is not known:**
   $$
   s = v t - \frac{1}{2} a t^2
   $$

These equations are applicable under the assumption of constant acceleration and are fundamental in solving various problems related to linear motion.

If you have a specific problem or need further clarification on how to apply these formulas, feel free to ask!
The formula $$ v = u + a t $$ calculates the final velocity of an object after a certain time with constant acceleration. Here, $$ v $$ is the final velocity, $$ u $$ is the initial velocity, $$ a $$ is the acceleration, and $$ t $$ is the time.

formulas. \( \begin{array}{l}\text { a. } v=u+a t \\ \text { - Workspace } \\ \text { + Check answer }\end{array} \)

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Physics Questions