Posted by **ROHIT** on Monday, August 6, 2012 at 1:08am.

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?

- Dynamics -
**MathMate**, Monday, August 6, 2012 at 7:40am
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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