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Answer:

(a) The final velocity of the car when it comes to rest is zero. The initial velocity is 24.6 m/s and the acceleration is -4.92 m/s² (negative because it's the deceleration due to braking). We can use the formula:

v = u + at

where v is final velocity, u is initial velocity, a is acceleration, and t is time.

In this case, v = 0, u = 24.6 m/s, and a = -4.92 m/s². Plugging in these values, we get:

0 = 24.6 - 4.92t

Solving for t, we get:

t = 24.6/4.92

t ≈ 5 seconds

Therefore, the car takes about 5 seconds to come to rest.

(b) We can use the formula:

s = ut + 1/2 at²

where s is the distance traveled, u is the initial velocity, a is the acceleration, and t is the time.

In this case, u = 24.6 m/s, a = -4.92 m/s², and t = 5 seconds (which we just calculated). Plugging in these values, we get:

s = 24.6 × 5 + 1/2 × (-4.92) × 5²

s = 123 - 61.5

s = 61.5 meters

Therefore, the car travels about 61.5 meters during the 5 seconds it takes to come to rest.