Question

A car decelerated from a speed of 20 m/s to rest in 8 seconds, falling short of its parking slot by 20 meters. By how much longer should the car have decelerated from the same speed so as to just reach the parking slot?

Answer 1

The car should have decelerated for approximately 4.375 seconds longer to just reach the parking slot.

Step-by-step explanation:

To find out how much longer the car should have decelerated to just reach the parking slot, we need to calculate the distance it would have covered during the additional deceleration. Since the car decelerated from a speed of 20 m/s to rest in 8 seconds, we can use the formula:

distance = initial velocity * time + (1/2) * acceleration * time^2

Substituting the given values, we get:

1. distance = 20 * 8 + (1/2) * acceleration * 8^2
2. distance = 160 + 32 * acceleration

Since the car fell short of its parking slot by 20 meters, we have:

160 + 32 * acceleration = 20

Solving this equation for acceleration:

32 * acceleration = 20 - 160

32 * acceleration = -140

acceleration = -140/32

Therefore, the car should have decelerated for an additional approximately 4.375 seconds to just reach the parking slot.