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

[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?

Homework Equations

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?

 

[AlephZero]

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.

 

[m2003]

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.