- #1

- 1,266

- 11

## Homework Statement

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.

## 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].