Final answer:
To find the lateral acceleration of the vehicle, divide the circumference of the skidpad by the time taken to travel around it. Then, use the formula for centripetal acceleration to calculate the acceleration. The lateral acceleration of the vehicle is approximately 7.38 m/s².
Step-by-step explanation:
To find the lateral acceleration of the vehicle, we need to first find the speed at which the vehicle is traveling around the skidpad. We can find this by dividing the circumference of the skidpad (πd) by the time it takes to travel the distance. The circumference is 2πr, where r is the radius of the skidpad (25 ÷ 2 = 12.5 m). So the circumference is 2π(12.5) = 25π m. Dividing this distance by the time (8.2 s), we get the speed of the vehicle as 25π ÷ 8.2 ≈ 9.62 m/s.
Next, we can use the formula for centripetal acceleration, which is given as a = v² / r, where a is the acceleration, v is the velocity, and r is the radius. Plugging in the values, we have a = (9.62)² / 12.5 ≈ 7.38 m/s².
Therefore, the lateral acceleration of the vehicle is approximately 7.38 m/s².