Which of the following graph is used for determining the instantaneous velocity from the slope? A. distance-time graph

B. x - t graph

C. both of these

D. none of these

B. x - t graph

Explanation:

A position-time (x-t) graph is a graph of the position of an object against (versus) time.

Generally, the slope of the line of a position-time (x-t) graph is typically used to determine or calculate the velocity of an object.

An instantaneous velocity can be defined as the rate of change in position of an object in motion for a short-specified interval of time. Thus, an instantaneous velocity is a quantity that can be found by measuring the slope of a line that is tangent to a point on the graph.

Hence, the x - t graph also referred to as the position-time graph is used for determining the instantaneous velocity from the slope.

For example;

Given that the equation of motion is S(t) = 4t² + 2t + 10. Find the instantaneous velocity at t = 5 seconds.

Solution.

Differentiating the equation, we have;

Substituting the value of "t" into the equation, we have;

S(5) = 42 m/s.

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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