A certain light truck can go around a curve having a radius of $100 m$ with a maximum speed of $16 m / s$ . To have the same acceleration, at what maximum speed (in $m / s$ ) can it go around a curve having a radius of $25 m$ ?

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Solution

Given:

Radius $R_{1} = 100 m$

Velocity, $v_{1} = 16 m / s$

Radius $R_{2} = 25 m$

According to given condition,

$f_{s m a x} = \frac{m v_{1}^{2}}{r_{1}} = \frac{m v_{2}^{2}}{r_{2}}$

$\Rightarrow \frac{m \times 16 \times 16}{100} = \frac{m v_{2}^{2}}{25}$

$v_{2} = 4 \times 2 = 8 m / s$

Final answer: 8 m/s

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A certain light truck can go around a curve having a radius of 100 m with a maximum speed of 16 m/s. To have the same acceleration, at what maximum speed (in m/s) can it go around a curve having a radius of 25 m?

Given: Radius R1=100 m Velocity, v1=16 m/s Radius R2=25 m According to given condition, fsmax=mv21r1=mv22r2 ⇒m×16×16100=mv2225 v2=4×2=8m/s Final answer: 8 m/s

A certain light truck can go around a curve having a radius of $100 m$ with a maximum speed of $16 m / s$ . To have the same acceleration, at what maximum speed (in $m / s$ ) can it go around a curve having a radius of $25 m$ ?