Question

Your vehicle takes 8.2 seconds to travel around a 25 m diameter skidpad. what is the lateral acceleration of the vehicle?

A) 1.93 m/s²
B) 2.05 m/s²
C) 3.06 m/s²
D) 4.12 m/s²

Answer 1

To calculate the lateral acceleration of the vehicle, we need to find the angular velocity of the vehicle using the formula ω = 2π × Number of revolutions / Time taken. With the angular velocity, we can then calculate the lateral acceleration using the formula Lateral acceleration = radius × (angular velocity)^2. Plugging in the values, the lateral acceleration of the vehicle is approximately 1.93 m/s².

Step-by-step explanation:

To calculate the lateral acceleration of the vehicle, we first need to find the angular velocity of the vehicle. The formula for angular velocity is given by:

Angular velocity (ω) = 2π × Number of revolutions / Time taken

Since the vehicle travels around a 25 m diameter skidpad, its circumference is given by:

Circumference = π × Diameter = π × 25 m

Using the formula for angular velocity, we can calculate:

ω = 2π × 1 / 8.2 s

Now that we have the angular velocity, we can calculate the lateral acceleration using the formula:

Lateral acceleration = radius × (angular velocity)^2

Since the skidpad has a diameter of 25 m, its radius is 12.5 m. Plugging in the values:

Lateral acceleration = 12.5 m × (ω)^2

After calculating the above expression, we find that the lateral acceleration of the vehicle is approximately 1.93 m/s².