Question

(Figure 1) shows a velocity-versus-time graph for the bicycle trips of two friends with respect to the parking lot where they started. Xena's position at time zero is 0 and Gabriele's position is 60 m. Write function x(t) for Gabriele with respect to Xena. Express your answer in meters in terms of t , where t is in seconds.

Answer 1

Based on the velocity-time graph, the function x(t) for Gabriele with respect to Xena is: x(t) = 60 -2t.

What is a velocity-time graph?

A velocity-time graph is a the graph of the change in velocity of an object or body with time.

The area under a velocity-time graph gives the displacement of the body within the given time interval.

From the given velocity-time graph:

The position, x, of Xena at time t, = v*t

x = 8t

The position of Gabriele at time t, = v*t

x =60 + 6t

Therefore, the function x(t) for Gabriele with respect to Xena is

x(t) = 60 + 6t - 8t

x(t) = 60 -2t

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