Question

A car is moving on a horizotal circular road of radius 144m with uniform speed 12m/s.It suddenly accelerates at 1m/s^2.Now the accelearation will be? a)1 b)2 c) √2

Answer 1

The acceleration will be c) √2.

Explanation:

Before the acceleration, centripetal acceleration, `a_c`, was the only acceleration. The formula for centripetal acceleration is

`a_c = v^2/r`

Plugging in the speed and radius,

`a_c = v^2/r = (12 m/s)^2/144 m = 1 m/s^2`

That acceleration would be pointed at the center of the circle as the car went followed the curve.

The linear acceleration of `1 m/s^2` that was added to the situation was tangential to the curve, therefore perpendicular to the centripetal acceleration. We can use Pythagoras to find the magnitude of the resultant of those 2 accelerations.

`a_"total" = sqrt((1 m/s^2)^2 + (1 m/s^2)^2) = sqrt(2 m^2/s^4)`

`a_"total" = sqrt(2) " "m/s^2`

I hope this helps,
Steve