A student wants to estimate the velocity of a cart at using only position measurements
MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A student wants to estimate the velocity of a cart at t=3.0s using only position measurements. The student can calculate the average velocity over Δt=0.20s centered on 3.0s or over Δt=0.02s centered on 3.0s. Which of the following best explains why the shorter time interval is expected to give a more accurate estimate of the cart’s velocity at 3.0s?
(a) Because the cart travels a smaller distance, the position-measurement error contributes less to the calculated velocity.
(b) Because making Δt very small in Δx/Δt mathematically makes the average velocity equal to the instantaneous velocity, regardless of measurement uncertainty.
(c) A shorter interval reduces the chance that the cart’s velocity changes appreciably during the measurement.
(d) Because reaction-time errors in starting and stopping the timing device are smaller for a shorter interval.