The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 7.9 seconds, if it reached a maximum speed of 10.0 m s-1?

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BlackTom AI · Accepted Answer

First, identify the portion of the motion described: during the first t1 = 7.9 s the helicopter accelerates from rest up to a maximum speed of 10.0 m/s, as shown by the rising ramp on the speed-time graph.
Next, recall the basic kinematics relation for constant acceleration: a = Δv / Δt, where Δv is the change in velocity and Δt is the time over which that change occurs.
Since the velocity starts at 0 m/s and reaches 10.0 m/s in 7.9 s, the change in velocity is Δv = 10.0 m/s − 0 m/s = 10.0 m/s.
Then substitute the values into the formula: a = 10.0 m/s ÷ 7.9 s.
Performing the division gives a ≈ 1.264... m/s^2. Rounding to three significant figures yields 1.27 m/s^2.
Finally, consider the assumptions: the graph shows a straight-line increase in speed during the first interval, which implies a constant acceleration over that time span. If the acceleration were not constant, the slope of the speed-time graph would not be uniform, and the simple Δv/Δt relation would not apply in the same way across the interval.

The graph shows the speed at which a remote controlled toy helicopter travels during a test flight along a straight flight path. What is the acceleration (in m s-2) of the helicopter during the first t1 = 7.9 seconds, if it reached a maximum speed of 10.0 m s-1?

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