Question

A blue car rounds a circular turn at a constant speed of $30m/s$. A grey van rounds the same turn at a constant speed of $15m/s$. How does the magnitude of the acceleration of the blue car compare to the magnitude of the acceleration of the grey van?

• A. The accelerations of both vehicles are zero, since neither is changing speed
• B. The magnitude of the blue car's acceleration is twice the magnitude of the grey van's acceleration
• C. The magnitude of the blue car's acceleration is four times the magnitude of the grey van's acceleration
• D. The magnitude of each car's acceleration is the same, but is not zero
• E. We do not have enough information to determine the relative magnitudes of acceleration for the cars in this questions

Answer 1

Answer: (C)

The magnitude of the blue car's acceleration is four times the magnitude of the grey van's acceleration

As the change in speed of both cars is zero therefore tangential acceleration of both cars will be zero .

now centripetal acceleration is given by

$a=v^2/r$ , where $r=$ radius and $v=$ linear velocity ,

for blue car $a_b={30}^2/r$

for grey van $a_g={15}^2/r$

radius is same for both as they round the same turn ,

so $a_b/a_g={30}^2/{15}^2=4$

or $a_b=4a_g$