Question

a car rounds a curve at a steady 50 km/h. if it rounds the same curve at a steady 70 km/h, will its acceleration be any different? explain.

Answer 1

Acceleration would be
`1.96` times the initial value.

Step-by-step explanation:

The vehicle is in a centripetal motion as it rounds the circular curve. Acceleration of the vehicle during the motion would be:

`\displaystyle a = (v^(2))/(r)`,

Where:

• 
  `v` is the speed of the vehicle, and
• 
  `r` is the radius of the curve.

In this question,
`r` stays the same since the vehicle is rounding the same curve. Acceleration of the vehicle would be proportional to the square of velocity.

The new velocity of the vehicle is
`(70 / 50)` times the original one. Hence, the new acceleration would be
`(70 / 50)^(2) = 1.96` times the original value.