Question

What is the instantaneous velocity v of the particle at t=10.0s?

Answer 1

The instantenous velocity is just the slope of the graph at a certain instant. Since the graph is a straight line, its instantenous velocity is uniform through out. v = dx / dt = (40 - 10) / (50 - 0) = 0.6 m/s.


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Answer 2

The instantaneous velocity of the particle is 0.600 m/s. Instantaneous velocity is the velocity of an object at any given time in its path.

FURTHER EXPLANATION

The instantaneous velocity of an object can be determined graphically in a position - time graph.

• If the velocity of the object is constant, the graph in  a position - time graph will be a straight  line and the instantaneous velocity will be equal to the slope or gradient of the line.
• If the velocity of the object is changing, the graph will be a curve and the instantaneous velocity can be determined from the slope of the curved line at any given moment.

To get the slope of a line, get the ratio of the rise and the run.

In the given problem, the velocity of the object is constant because its position - time graph shows a straight line. As such, the instantaneous velocity will be equal to the average velocity.

To solve for the average velocity, use the equation below:

$average \ velocity \ = \frac{displacement \ ( \Delta y)}{ time \ (\Delta x)}$

Using data from the graph,

$average \ velocity \ = \frac{40\ m - 10 \ m}{50 \ s \ - 0 \ s} \\average \ velocity \ = \frac{30 \ m}{50 \ s}\\ \\ \boxed {average \ velocity = 0.6 \frac{m}{s}}$

The instantaneous velocity expressed with 3 significant figures like the given in the problem, therefore, is 0.600 m/s.

LEARN MORE

• Position - Time Graph https://brainly.com/question/11533012
• Acceleration https://brainly.com/question/4134594
• Velocity - Time Graph https://brainly.com/question/4710544

Keywords: instantaneous velocity, position - time graph