Question

A race-car drives around a circular track of radius RRR. The race-car speeds around its first lap at linear speed v_iv i ​ v, start subscript, i, end subscript. Later, its speed increases to 4v_i4v i ​ 4, v, start subscript, i, end subscript. How does the magnitude of the car's centripetal acceleration change after the linear speed increases

Answer 1

Answer and Explanation: Centripetal Acceleration is the change in velocity caused by a circular motion. It is calculated as:

$a_{c}=\frac{v^{2}}{r}$

v is linear speed

r is radius of the curve the object in traveling along

For its first lap:

$a_{c}_{1}=\frac{v_{i}^{2}}{R}$

After a while:

$a_{c}_{2}=\frac{(4v_{i})^{2}}{R}$

$a_{c}_{2}=\frac{16v_{i}^{2}}{R}$

Comparing accelerations:

$\frac{a_{c}_{2}}{a_{c}_{1}}=\frac{16.v_{i}^{2}}{R}.\frac{R}{v_{i}^{2}}$

$\frac{a_{c}_{2}}{a_{c}_{1}}=\frac{16.v_{i}^{2}}{R}.\frac{R}{v_{i}^{2}}$

$\frac{a_{c}_{2}}{a_{c}_{1}}=16$

$a_{c}_{2}=16a_{c}_{1}$

With linear speed 4 times faster, centripetal acceleration is 16 times greater.