(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A racehorse accelerates from rest at time t = 0.0 s, out of its starting stalls with a time dependent acceleration a given by a = 1.7α - 0.6β t. It accelerates so until time = 4 s when it reaches a consant racing speed of [tex]v = 15.5 ms^{–1}[/tex].

(a)Use this information to first estabilsh how the constants α and β are related to each other.

(b)Using the definition of acceleration as the time rate of change of velocity, find an expression for the velocity and use it to establish the values of the consants α and β from the information available above. Be sure to include the correct SI units with the values of each of these constants.

3. The attempt at a solution

(a)The answer has to be [tex]\alpha = 1.41 \beta[/tex] and when I solve the following for alpha in terms of beta

[tex]a =1.7 \alpha - 0.6 \beta 4[/tex]

[tex]a=v/t = 15.5/4=3.87[/tex] so

[tex]3.9= 1.7 \alpha -2.4 \beta[/tex]

[tex]\alpha = 2.29+1.41 \beta[/tex]

So it should be [tex]\alpha = 2.29+1.41 \beta[/tex], but why does the answers suggest that is should be [tex]\alpha = 1.41 \beta[/tex]? What happens to the term 2.29?

(b)It wouldn't work if I substitute [tex]\alpha= 1.41 \beta[/tex] into that formual like [tex]1.41 \beta = 2.29+1.41 \beta[/tex]. So how do I use [tex]\alpha = 2.29+1.41 \beta[/tex] (definition of acceleration as the time rate of change of velocity) to find the vales of alpha & beta?

Btw, the answer should be [tex]\alpha = 4.56 ms^{-2}, \beta=3.23 ms^{-3}[/tex].

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# Homework Help: Acceleration and velocity

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