Question

NEED HELP ASAP

Answer 1

Answer: 20.73 m/s

Explanation:

The centripetal force is given by the following equation:

$F_{c}=m a_{c}$ (1)

Where:

$F_{c}=2600 N$ is the centripetal force

$m=1200 kg$ is the mass of the car

$a_{c}$ is the centripetal acceleration

Isolating $a_{c}$:

$a_{c}=\frac{F_{c}}{m}$ (2)

$a_{c}=\frac{2600 N}{1200 kg}$ (3)

$a_{c}=2.16 m/s^{2}$ (4)

Now, there is a relation between the centripetal acceleration and the tangential velocity:

$a_{c}=\frac{V^{2}}{r}$ (5)

Where $V$ is the tangential velocity and $r$ is the radius of the circular path, which can be found if we know its length $l=1.25 km=1250 m$:

$l=2 \pi r$ (6)

$r=\frac{l}{2 \pi}$ (7)

$r=\frac{1250 m}{2 \pi}$ (8)

$r=198.94 m$ (9)

Substituting (4) and (8) in (5)

$2.16 m/s^{2}=\frac{V^{2}}{198.94 m}$ (5)

Finding $V$:

$V=20.729 m/s \approx 20.73 m/s$