A car is traveling along a straight road at a velocity of +36.0 m/s when its engine cuts out. 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 velocity of the car at the end of the fifteen-second period is +24.5 m/s. The ratio of the average acceleration values is a1/a2 = 1.74. Find the velocity of the car at the end of the initial ten-second interval.

V = 27.07 m/s

Explanation:

Given that a car is traveling along a straight road at a velocity of +36.0 m/s when its engine cuts out. And For the next ten seconds the car slows down, and its average acceleration is a1.

To calculate the acceleration, let use the 1st equation of motion.

V = U - at

As the car is going to rest, V = 0 and a = negative.

V = 36 - a1 × 10

V = 36 - 10a1 (1)

- 10a1 = V - 36

a1 = (36 - V) / 10

Given that For the next five seconds the car slows down further, and its average acceleration is a2. The velocity of the car at the end of the fifteen-second period is +24.5 m/s.

Using the same formula again

V = U - at

24.5 = 36 - 10a1 - a2 × 5

24.5 - 36 = - 10a1 - 5a2

- 11.5 = -( 10a1 + 5a2)

11.5 = 10a1 + 5a2 (2)

But The ratio of the average acceleration values is a1/a2 = 1.74.

a1 = 1.74a2 (3)

Substitute a1 in equation 2

11.5 = 10( 1.74a2) + 5a2

11.5 = 17.4a2 + 5a2

11.5 = 22.4a2

a2 = 11.5/22.4

a2 = 0.5134 m/s^2

Substitutes a2 in equation 3

a1 = 1.74 × 0.5134

a1 = 0.893 m/s^2

Substitutes a1 into equation 1

V = 36 - 10(0.893)

V = 36 - 8.93

V = 27.07 m/s

Therefore, the velocity of the car at the end of the initial ten-second interval is 27.07 m/s

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min