A 1.3 X 10^3 kg car traveling with a speed of 2.5 m/s executes a turn with a

7.5 m radius of curvature. Calculate the centripetal acceleration of the car and
the centripetal force acting on the car.

0.83

To calculate the centripetal acceleration of the car, we can use the formula:

a = v^2 / r

where:
a = centripetal acceleration
v = velocity of the car
r = radius of curvature

Plugging in the values:
v = 2.5 m/s
r = 7.5 m

a = (2.5 m/s)^2 / 7.5 m
a = 6.25 m^2/s^2 / 7.5 m
a = 0.8333 m/s^2

Therefore, the centripetal acceleration of the car is 0.8333 m/s^2.

Now, to calculate the centripetal force acting on the car, we can use the formula:

F = m * a

where:
F = centripetal force
m = mass of the car
a = centripetal acceleration

Given:
m = 1.3 x 10^3 kg (mass of the car)
a = 0.8333 m/s^2 (centripetal acceleration)

F = (1.3 x 10^3 kg) * (0.8333 m/s^2)
F = 1083.33 kg*m/s^2

Therefore, the centripetal force acting on the car is 1083.33 N.

To calculate the centripetal acceleration of the car, we can use the formula:

a = v^2 / r

where:
a is the centripetal acceleration,
v is the velocity of the car,
r is the radius of curvature.

In this case, the velocity (v) of the car is given as 2.5 m/s, and the radius of curvature (r) is given as 7.5 m.

Let's substitute these values into the formula:

a = (2.5 m/s)^2 / 7.5 m

Using a calculator, simplify the equation:

a = 6.25 m^2/s^2 / 7.5 m
a = 0.8333 m/s^2

So, the centripetal acceleration of the car is approximately 0.8333 m/s^2.

To calculate the centripetal force acting on the car, we can use the formula:

F = m * a

where:
F is the centripetal force,
m is the mass of the car,
a is the centripetal acceleration.

In this case, the mass (m) of the car is given as 1.3 x 10^3 kg, and the centripetal acceleration (a) we calculated earlier is approximately 0.8333 m/s^2.

Let's substitute these values into the formula:

F = (1.3 x 10^3 kg) * (0.8333 m/s^2)

Using a calculator, simplify the equation:

F = 1083.329 kg * m/s^2

So, the centripetal force acting on the car is approximately 1083.329 N.

0.83 m/s^2

1049 N