# Dynamics

A car travels around a horizontal circular track of radius 45m.If the car increases its speed at a constant rate of 1.2m/s2 starting from rest, determine the time needed for it to reach an acceleration of 1.4m/s2. What is its speed at this instant?

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1. Assuming 1.4m/s^2 is the combined radial acceleration (ar) and tangential (at).

Note that the two accelerations are orthogonal (perpendicular) so that the combined acceleration can be found using Pythagoras theorem.

ar=v²/r=v²/45
at=1.2
where v=tangential velocity

When the combined acceleration = 1.4
we have
1.4²=1.2²+(v²/45)²
v^4=(1.96-1.44)*45^2
=1053
=> v=5.7 m/s

At at=1.2 m/s from rest, it takes
t=5.7/1.2=4.75 seconds

check the numbers.

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