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Chapter 2: Problem 211

In a uniformly accelerated motion the slope of velocity - time graph gives .... (A) The instantaneous velocity (B) The acceleration (C) The initial velocity (D) The final velocity

Short Answer

Expert verified
In a uniformly accelerated motion, the slope of the velocity-time graph gives the acceleration. The relationship between velocity, time, and acceleration can be given by the equation \(v = v_0 + at\), where the slope is the acceleration (a). Thus, the correct answer is (B) The acceleration.

Step by step solution

01

Understand the relationship between velocity, time, and acceleration in uniformly accelerated motion.

In uniformly accelerated motion, the acceleration is constant. The relationship between velocity (v), initial velocity (v0), acceleration (a), and time (t) can be given by the equation: \(v = v_0 + at\)
02

Plot a velocity-time graph from the velocity equation.

According to the equation from step 1, the velocity is a linear function of time. The graph of \(v\) against \(t\) will be a straight line, with the initial velocity as the y-intercept and the acceleration as the slope.
03

Analyze the slope of the velocity-time graph.

The slope of the graph is the quantity that is multiplied by the time (t) variable. In our equation: \(v = v_0 + at\), the slope is the acceleration (a).
04

Choose the appropriate answer.

Upon analyzing the velocity-time graph, we conclude that the slope of the velocity-time graph in a uniformly accelerated motion gives the acceleration. So, our answer is: (B) The acceleration

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Most popular questions from this chapter

An object is projected with initial velocity of \(100 \mathrm{~ms}^{-1}\) and angle of 60 . Find the vertical velocity when its horizontal displacement is \(500 \mathrm{~m} .\left(\mathrm{g}=10 \mathrm{~ms}^{-1}\right)\) (A) \(13.35 \mathrm{~ms}^{-1}\) (B) \(-13.35 \mathrm{~ms}^{-1}\) (C) \(-8.65 \mathrm{~ms}^{-1}\) (D) \(98 \mathrm{~ms}^{-1}\)

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