Question

The light turns green and you press your foot on the accelerator. Your car, starting from rest, gains a uniform acceleration of 2m/s^2 until you see on the speedometer
that you're going 45 miles per hour (1 mile - 1.61km). You continue to travel at 45 miles per hour for 20 seconds. Then you see a stop sign and apply the brakes, stopping
your car with a uniform acceleration within 5 seconds. What is the average velocity of your car?

Answer 1

Here, we are required to find the average velocity of the car.

Therefore, the average velocity, Va = 15.74m/s.

• The time taken to attain a speed of 45miles per hour (where 1mile = 1.61km) can be calculated from V = U + at.
• Therefore, since the car starts from rest, U = 0.
• And V = (45 × 1.61 × 1000)/3600 = 20.125m/s.
• Therefore, time, t1 = (20.125 -0)/2 = 10.06seconds.
• and, the distance travelled, D1 = (20.125)²/2×2
• therefore, D1 = 101.25

• Secondly, the car travels at constant speed of 45 miles per hour, i.e 20.125 for the next 20 seconds.
• The distance, D2 covered = 20.125 × 20 = 400.25meters.

• And lastly, during deceleration, the car is stopped with uniform deceleration within 5seconds.
• uniform acceleration,a3 = 20.125/5 = 4.025
• the distance travelled is given by :
• D3 = (20.125)²/2× 4.025.
• D3 = 50.31meters.

Therefore the total distance travelled, D is:

D = D1 + D2 + D3

D = (101.25 + 400.25 + 50.31)meters.

D = 551.81meters.

and the total time of travel ,T = t1 + t2 + t3

therefore, T = 10.06 + 20 + 5

T = 35.06seconds.

Therefore, the Average velocity of the car is:

Va = D/T

therefore, Va = 551.81/35.06

Va = 15.74 m/s

Therefore, the average velocity, Va = 15.74m/s.

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