When the driver first notices the garbage can, the distance between the car and the can is x2-x0=d. You have found that the distance traveled by the car before the brakes are applied is v0t. Find the distance x2-x1 traveled by the car after the brakes are applied.

The distance travelled when the brakes are applied, (x2 - x1) = (d - v₀t)

Acceleration of the car after brakes are applied = - [v₀² / (d - v₀t) ]

Explanation:

The driver initially distance d, away from the can, travels a further distance of v₀t.

New distance of the driver from the can = (d - v₀t)

And it is said that the driver stops just before the can,

Hence, the distance travelled when the brakes are applied, x2 - x1 = (d - v₀t)

The acceleration after the application if the brakes is obtained from the equations of motion.

Distance travelled = (d - v₀t)

Initial velocity before the application of brakes = v₀ m/s

Final velocity = 0 m/s

acceleration = ?

√ ²

But we know acceleration is negative, since it is deceleration.

Using v₀² = 0 - 2a (d - v₀t)

a = - [v₀² / (d - v₀t) ]