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Chapter 11: Problem 5

Given the acceleration of an object and its initial velocity, how do you find the velocity of the object, for \(t \geq 0 ?\)

Short Answer

Expert verified
Answer: The formula to find the velocity of an object at any given time, given its acceleration and initial velocity, is \(v(t) = v_0 + at\), where \(v(t)\) is the velocity at time \(t\), \(v_0\) is the initial velocity, and \(a\) is the constant acceleration.

Step by step solution

01

1. Identify the given variables

From the problem, we know the initial velocity and acceleration of an object. Let's denote the initial velocity as \(v_0\) and the acceleration as \(a.\)
02

2. Understand the velocity formula for an object under constant acceleration

The formula for calculating the velocity of an object under constant acceleration is given by: $$v(t) = v_0 + at$$ where: - \(v(t)\) is the velocity of the object at a specific time, \(t\) - \(v_0\) is the initial velocity of the object - \(a\) is the constant acceleration of the object - \(t\) is the time at which we want to find the velocity We can use this formula to calculate the velocity of the object at any given time \(t \geq 0.\)
03

3. Calculate the velocity of the object at time t

We have the initial velocity \(v_0\), the acceleration \(a\), and a given time \(t\). We can now plug these values into the velocity formula to find the velocity of the object at time \(t\): $$v(t) = v_0 + at$$ This expression gives the velocity of the object at any time \(t \geq 0.\) Make sure to use the appropriate units for velocity, acceleration, and time when making the calculations. In conclusion, by knowing the acceleration and initial velocity of an object, we can find its velocity at any time \(t \geq 0\) using the formula \(v(t) = v_0 + at\).

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