Question

A car is traveling along a straight road at a velocity of 30m/s when its engine cuts off. For the next ten seconds, the car slows down, and its average acceleration is a₁. For the next five seconds, the car slows down further, and its average acceleration is a₂. The ratio of the average acceleration values is a₁/a₂=1.5. Find the velocity of the car at the end of the initial ten-second interval.​

Answer 1

The velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.

Initial velocity of the car

v = u + at

after 10 seconds;

v = 30 + 10a₁  --(1)

after 5 seconds

v₂ = v + 5a₂ ---- (2)

solve (1) and (2) together

v₂ = 30 + 10a₁ + 5a₂

but a₁/a₂=1.5

a₁ = 1.5a₂

v₂ = 30 + 10(1.5a₂) + 5a₂

v₂ = 30 + 15a₂ + 5a₂

v₂ = 30 + 20a₂

from equation (2), v₂ = v + 5a₂

v + 5a₂ = 30 + 20a₂

v = 15a₂ + 30

Thus, the velocity of the car at the end of the initial ten-second interval is 15a₂ + 30.

Learn more about velocity here: brainly.com/question/4931057

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