## Problem You are given a list of GPS readings for a vehicle: each reading has a timestamp (in seconds) and a position `(x, y)` in meters. Compute the instantaneous velocity (m/s) at each interior point using central differences, and return the average speed over the full trace. ```python from dataclasses import dataclass @dataclass class GPSReading: t: float # seconds x: float y: float def compute_velocities(readings: list[GPSReading]) -> tuple[list[float], float]: # Returns (instantaneous_speeds, average_speed) # instantaneous_speeds[0] and [-1] should use forward/backward differences pass ``` **Example:** ``` readings = [ GPSReading(0, 0, 0), GPSReading(1, 3, 4), # distance from prev = 5m GPSReading(3, 9, 12), # distance from prev = 10m over 2s ] -> speeds = [5.0, 5.0, 5.0], avg = 5.0 ``` ## Follow-ups 1. What is the difference between central, forward, and backward finite-difference approximations for velocity? 2. GPS readings often have noise. What smoothing technique would you apply before computing velocities? 3. How would you compute acceleration from the velocity array? 4. If timestamps are not uniformly spaced, how does that affect the finite-difference formula?

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Vehicle Velocity: Compute Instantaneous and Average Velocity from a GPS Trace

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Problem You are given a list of GPS readings for a vehicle: each reading has a timestamp (in seconds) and a position (x, y) in meters. Compute the instantaneous velocity (m/s) at each interior point using central differences, and return the average speed over the full trace. Example: Follow-ups What is the difference between central, forward, and backward finite-difference approximations for velocity? GPS readings often have noise. What smoothing technique would you apply before computing veloci…

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This is a candidate experience report from a applied intuition interview during the onsite round.

It covers the following topics: Coding, Arrays, Onsite .

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Vehicle Velocity: Compute Instantaneous and Average Velocity from a GPS Trace

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