Question

A certain light truck can go around a curve having a radius of 119 m with a maximum speed of 30 m/s. To have the same acceleration, at what maximum speed can it go around a curve having a radius of 59.5 m

Answer 1

The maximum speed is 21.1 m/s

Step-by-step explanation:

Given that,

Radius of curve = 119 m

Maximum speed = 30 m/s

New radius = 59.5 m

We need to calculate the maximum acceleration

Using formula of acceleration

`a_(c)=(v^2)/(r)`

Where, v = maximum speed

r = radius

a = acceleration

Put the value into the formula

`a_(c)=(30^2)/(119)`

`a_(c)=7.5\ m/s^2`

We need to calculate the maximum speed

Using formula of speed

`v_(max)=√(a* r)`

Put the value into the formula

`v_(max)=√(7.5*59.5)`

`v_(max)=21.1\ m/s`

Hence, The maximum speed is 21.1 m/s