# Solve Simple Motion Prob: Inst. Speed of Bicycle 5m

• student12phys
In summary, two physics students were trying to determine the instantaneous speed of a bicycle at the 5m mark in a 1000m sprint. Using a stopwatch to measure the time taken for the bicycle to cover the first 10m and assuming constant acceleration, they calculated the acceleration to be .625m/s^2. However, their attempt at solving for the instantaneous velocity at 5sec using the equation 1/2 a t^2 was incorrect as they used the average velocity over 4sec instead of the final velocity. The correct equation for constant acceleration starting from rest is displacement = 1/2 a t^2.
student12phys

## Homework Statement

Two physics students are trying to determine the instantaneous speed of a bicycle 5m from the start of a 1000m sprint. They use a stopwatch to measure the time taken for the bicyble to cover the first 10m. If the acceleration was constant, and the measured time was 4sec, what was the instantaneous speed of the bicyle at 5m mark?

## The Attempt at a Solution

Method 1:
Find acceleration:
a=change in velocity/change in time
=(displacement/time) /time
= displacement/time^2
= (10-0)/(4-0)^2
=.625m/s^2
Find instantaneous velocity at 5sec:
5 x .625 = 3.125m/s

BUt the answer is wrong. WHy?

Accel = change in velocity / change in time - that's right (equation 1).
Velocity = change in distance / change in time - that's also right.

But when you say "velocty = (10-0)/4" you are finding the AVERAGE velocity over the 4 sec, not the FINAL velocity that you need in equation 1.

The correct equation for constant acceleration is starting from rest is displacement = 1/2 a t^2 Check back to your textbook or notes on motion with constant acceleration.

Method 1 is incorrect because it assumes that the acceleration is constant throughout the entire 1000m sprint. In reality, the acceleration of the bicycle may change as the rider pedals and adjusts their speed. To accurately determine the instantaneous speed at the 5m mark, the students would need to take multiple measurements at different points along the sprint and use calculus to find the derivative of the displacement-time curve at the 5m mark. This would provide the instantaneous velocity at that specific point. Another approach could be to use a high-speed camera to capture the movement of the bicycle and use video analysis techniques to calculate the instantaneous velocity at the 5m mark.

## What is a Simple Motion Problem?

A Simple Motion Problem is a physics problem that involves the motion of an object in a straight line with a constant speed or acceleration.

## What is the Instantaneous Speed of a Bicycle?

The Instantaneous Speed of a bicycle is the speed at a specific moment in time, rather than an average speed over a period of time. It is also known as the instantaneous velocity.

## How is the Instantaneous Speed of a Bicycle Calculated?

The Instantaneous Speed of a bicycle can be calculated by dividing the distance traveled by the time taken at a specific moment in time. This can be represented by the equation: Instantaneous Speed = Distance / Time.

## What is the Unit of Measurement for Instantaneous Speed?

The unit of measurement for Instantaneous Speed is meters per second (m/s) in the metric system and feet per second (ft/s) in the imperial system.

## How Does a Bicycle's Instantaneous Speed Change during Motion?

A bicycle's Instantaneous Speed can change during motion due to factors such as acceleration, deceleration, or changes in terrain. It can also remain constant if the bicycle is traveling at a constant speed.

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