Question

NEED HELP ASAP

Vin Diesel is filming yet another Fast and Furious movie. He is driving a 1200kg sports car around a circular track of 1.25km. If the magnitude of the centripetal force is 2600N, what is the car’s tangential speed?

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Answer 1

Answer: 20.73 m/s

Step-by-step 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)=(F_(c))/(m)` (2)

`a_(c)=(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)=(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=(l)/(2 \pi)` (7)

`r=(1250 m)/(2 \pi)` (8)

`r=198.94 m` (9)

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

`2.16 m/s^(2)=(V^(2))/(198.94 m)` (5)

Finding
`V`:

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