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Chapter 2: Problem 57

The velocity of a body depends on time according to the equation \(v=20+0.1 t^{2}\). The body is undergoing (A) Uniform acceleration (B) Uniform retardation (C) Non-uniform acceleration (D) Zero acceleration

Short Answer

Expert verified
The acceleration function is \(a(t) = 0.2t\), which is neither constant nor zero. The body is undergoing (C) Non-uniform acceleration.

Step by step solution

01

Determine the velocity function

We are given the velocity of a body as a function of time: \(v(t) = 20 + 0.1t^2\).
02

Find the acceleration function

To find the acceleration as a function of time, we need to take the derivative of the velocity function with respect to time: \(a(t) = \frac{d}{dt}(20 + 0.1t^2)\) Using basic calculus rules to differentiate the given function, we get: \(a(t) = 0.2t\)
03

Determine the type of acceleration

Now that we have the acceleration function, \(a(t) = 0.2t\), we need to determine the type of acceleration the body is undergoing: (A) Uniform acceleration: The acceleration function is constant. (B) Uniform retardation: The acceleration function is a constant negative value. (C) Non-uniform acceleration: The acceleration function changes with time. (D) Zero acceleration: The acceleration function is zero. When we observe the acceleration function \(a(t) = 0.2t\), we can see that it is not constant nor zero, meaning it cannot be uniform acceleration or zero acceleration. Additionally, as the function is positive for positive values of t (assuming the acceleration is in the same direction) and increasing, it cannot represent uniform retardation. Therefore, the body is undergoing: (C) Non-uniform acceleration

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Most popular questions from this chapter

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