A race car traveling at 50 m/s is uniformly accelerated to a velocity of 25 m/s over a 10-second interval. A. What is the acceleration of the car? B. What is its displacement during this time?

4a. –2.5 m/s²

4b. 375 m

5. 7.5 s

Explanation:

4. The following data were obtained from the question:

Initial velocity (u) = 50 m/s

Final velocity (v) = 25 m/s

Time (t) = 10 s

Acceleration (a) =?

Displacement (s) =?

4a. Determination of the acceleration of the car.

Initial velocity (u) = 50 m/s

Final velocity (v) = 25 m/s

Time (t) = 10 s

Acceleration (a) =?

a = (v – u) /t

a = (25 – 50)/10

a = –2.5 m/s²

The negative sign indicate that the car is decelerating.

4b. Determination of the displacement of the car.

Initial velocity (u) = 50 m/s

Final velocity (v) = 25 m/s

Time (t) = 10 s

Displacement (s) =?

s = (v + u)t / 2

s = (25 + 50) × 10 / 2

s = (75 × 10) / 2

s = 750 / 2

s = 375 m

Thus, the displacement of the car is 375 m

5. The following data were obtained from the question:

Initial velocity (u) = 30 m/s

Final velocity (v) = 0 m/s

Acceleration (a) = – 4m/s²

Time (t) =?

The time taken for the car to stop can be obtained as follow:

v = u + at

0 = 30 + (–4 × t)

O = 30 – 4t

Collect like terms

0 – 30 = –4t

–30 = –4t

Divide both side by –4

t = –30 / –4

t = 7.5 s

Thus, it will take 7.5 s for the car to completely stop.

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