A particle moves according to the equation; x = 10t2, where x is in meters and t is in seconds. Find the velocity for the time interval from 2.0 s to 2.1 s. (a) 0.1 m/s (b) 42 m/s (c) 44.1 m/s (d) 40 m/s (e) 2.0 m/s 11
Question
A particle moves according to the equation; x = 10t2, where x is in meters and t is in seconds. Find the velocity for the time interval from 2.0 s to 2.1 s. (a) 0.1 m/s (b) 42 m/s (c) 44.1 m/s (d) 40 m/s (e) 2.0 m/s 11
Solution
The velocity of a particle is given by the derivative of the position function. In this case, the position function is x = 10t^2.
Step 1: Differentiate the position function to get the velocity function. The derivative of t^2 is 2t, so the velocity function is v = 20t.
Step 2: To find the velocity at a specific time, substitute that time into the velocity function.
For t = 2.0 s, v = 202.0 = 40 m/s. For t = 2.1 s, v = 202.1 = 42 m/s.
The velocity for the time interval from 2.0 s to 2.1 s is the change in velocity over the change in time.
Step 3: Calculate the change in velocity. Δv = v(2.1) - v(2.0) = 42 m/s - 40 m/s = 2 m/s.
Step 4: Calculate the change in time. Δt = 2.1 s - 2.0 s = 0.1 s.
Step 5: Divide the change in velocity by the change in time to get the average velocity over the time interval.
v_avg = Δv/Δt = 2 m/s / 0.1 s = 20 m/s.
However, none of the options match this result. There might be a mistake in the problem or the options.
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