Question

You are driving your car around a roundabout when you get a flat tire and you decelerate at a constant rate to a stop. The diameter of the roundabout is 100m. It takes you 20 sec to come to a complete stop. While slowing down, you continue to drive in a circle and you stop halfway around the loop. What must your speed have been before the pop?

Answer 1

To calculate the initial speed of the car before the tire got flat, we used the circumference of the roundabout to determine the distance covered while decelerating and applied the formula for constant deceleration considering the time it took to come to a stop.

Step-by-step explanation:

The student's question involves calculating the initial speed of the car before the tire got flat while driving around a roundabout with constant deceleration. Given the diameter of the roundabout is 100 meters and the car comes to a stop halfway around, we can determine the circumference of the roundabout and the distance the car covers while decelerating.

Firstly, let's calculate the circumference of the roundabout using the formula C = πd, where C is the circumference and d is the diameter. C = π × 100m.

To find the initial speed, we use the formula for constant deceleration, v = u + at, where v is the final velocity (0 m/s, since the car stops), u is the initial velocity (what we are trying to find), a is the deceleration, and t is the time taken to stop.

Assuming the car stopped halfway around the roundabout, it covered a distance equivalent to half the circumference, so the distance s is s = C/2.

Using the equation s = ut + 1/2
`at^2`, we can find u since s, a, and t are known. Since the initial and final points are on a curve, this implies a centripetal component, but the question confines to linear deceleration.