A Car With An Initial Speed Of 36 Km/h Accelerates At A Uniform Rate Of 2.4 M/s^2 For 2.5 Seconds. What (2024)

Answer:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Step-by-step explanation:

Solve for y:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of y:

-x + x^2 + y (2 i x + i) - y^2 = 0

Multiply both sides by -1:

x - x^2 + y (-2 i x - i) + y^2 = 0

Subtract -x^2 + x from both sides:

y (-2 i x - i) + y^2 = x^2 - x

Add 1/4 (-2 i x - i)^2 to both sides:

1/4 (-2 i x - i)^2 + y (-2 i x - i) + y^2 = 1/4 (-2 i x - i)^2 - x + x^2

Write the left hand side as a square:

(1/2 (-2 i x - i) + y)^2 = 1/4 (-2 i x - i)^2 - x + x^2

Take the square root of both sides:

1/2 (-2 i x - i) + y = sqrt(1/4 (-2 i x - i)^2 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = 1/2 (2 i x + i) + sqrt((((-2 i) x - i)^2)/4 - x + x^2) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

y = 1/2 (2 i x + i) + sqrt((-2 x - 1/4)) or 1/2 (-2 i x - i) + y = -sqrt(1/4 (-2 i x - i)^2 - x + x^2)

Subtract 1/2 (-2 i x - i) from both sides:

y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((((-2 i) x - i)^2)/4 - x + x^2)

1/4 (-2 i x - i)^2 - x + x^2 = -2 x - 1/4:

Answer: y = sqrt(-2 x - 1/4) + 1/2 (2 i x + i) or y = 1/2 (2 i x + i) - sqrt((-2 x - 1/4))

________________________

Solve for x:

(x + (0 + i) y)^2 = x + (0 - i) y

Subtract -i y + x from both sides:

-x + (i y + x)^2 + i y = 0

Expand and collect in terms of x:

x^2 + x (2 i y - 1) + i y - y^2 = 0

Subtract -y^2 + i y from both sides:

x^2 + x (2 i y - 1) = y^2 - i y

Add 1/4 (2 i y - 1)^2 to both sides:

x^2 + x (2 i y - 1) + 1/4 (2 i y - 1)^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Write the left hand side as a square:

(x + 1/2 (2 i y - 1))^2 = 1/4 (2 i y - 1)^2 - i y + y^2

Take the square root of both sides:

x + 1/2 (2 i y - 1) = sqrt(1/4 (2 i y - 1)^2 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = 1/2 (-2 i y + 1) + sqrt((((2 i) y - 1)^2)/4 - i y + y^2) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

x = 1/2 (-2 i y + 1) + sqrt(((-2 i) y + 1/4)) or x + 1/2 (2 i y - 1) = -sqrt(1/4 (2 i y - 1)^2 - i y + y^2)

Subtract 1/2 (2 i y - 1) from both sides:

x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((2 i y - 1)^2)/4 - i y + y^2)

1/4 (2 i y - 1)^2 - i y + y^2 = -2 i y + 1/4:

Answer: x = sqrt((-2 i) y + 1/4) + 1/2 (-2 i y + 1) or x = 1/2 (-2 i y + 1) - sqrt(((-2 i) y + 1/4))

Answer:

Step-by-step explanation:

A Car With An Initial Speed Of 36 Km/h Accelerates At A Uniform Rate Of 2.4 M/s^2 For 2.5 Seconds. What (2024)

FAQs

What is the acceleration of a car when its velocity increases from 36 km h to 108 km h in 10s? ›

similarly, 36km/hr=10m/sec. acceleration is change in velocity per unit time. a=(30-10)/10sec. =2m/sec^2.

What is the average acceleration of a car that accelerates from rest to 48m s in 6 seconds? ›

The average acceleration of a car that accelerates from rest to 48 m/s in 6 seconds is 8 m/s². During this time, the car travels a distance of 144 meters. Explanation: The question asks for the average acceleration of a car and the distance it traveled during a specific time period.

What is the distance covered by a car that accelerates uniformly from 18 km per hour to 36 km per hour in 5 seconds? ›

Therefore, the distance traveled by car is 37.5 m. Q. A car accelerates uniformly from 18 km/hr to 36km/hr in 5s.

What is the average speed of car when it increases its speed with uniform rate from 20 km h to 50 km h in 10 seconds? ›

Hence, average speed of car is 34.99 km/h.

What is the distance travelled by a car attains velocity of 36 km h after accelerating uniformly from rest in 5 second? ›

Hence, acceleration is 2 m s 2 and Distance covered = 25 m.

What is the acceleration of a car if the speed of the car has increased from 25 km per hour to 40 km per hour in one minute? ›

Expert-Verified Answer

The time taken is 1 minute. in order to convert the km/hr to m/s we have to multiply by 5/18. The time taken is 1 min which is 60 seconds. Therefore the final answer is 0.069333 meter per second.

What is acceleration of a car accelerates uniformly from 18 km h to 72km hr in 5s? ›

⇒ 15 m/s. ⇒ Acceleration of the car (a) = 15/5 = 3m/s2.

How do you find the average acceleration of a car? ›

Average Acceleration Formula: The formula for average acceleration is the change in velocity, the final velocity minus the initial velocity, divided by the change in time.

How do you calculate accelerating speed? ›

Acceleration (a) is the change in velocity (Δv) over the change in time (Δt), represented by the equation a = Δv/Δt. This allows you to measure how fast velocity changes in meters per second squared (m/s^2).

What is the distance a train accelerates uniformly from 36 km per hour to 72 km per hour? ›

Answer: s = ut + (1/2)at², where s is the distance traveled. Therefore, the total distance traveled by train in the 20s is 300m.

What is the acceleration of a car accelerates uniformly from 18 km to 36 km in 5s? ›

Therefore, the acceleration and the distance covered by the car in that time are 1 m / s 2 and. 5 m respectively.

What is a car accelerating uniformly from 20 km/h to 35 km/h in 5 seconds? ›

20 km/hr=20*5/18=5.5m/s. 35 km/hr=35*5/18=9.7m/s. time =5 seconds. distance covered=110.5m.

What is the acceleration of a car increase its speed from 20 km to 50 km in 10 second? ›

Its acceleration is. 30 ms−2.

How much distance is covered by the car at rest accelerates uniformly to a speed of 144 km h in 20 s? ›

Hence, the distance covered (S) =400 m and option B is the correct answer .

Is accelerating at constant speed? ›

Answer and Explanation: If a body is moving with constant speed in a circle, then yes, that body has acceleration. However, if the body is moving with constant speed in a straight line, then no, that body has no acceleration.

What is the work to be done to increase the velocity of a car from 36 km h to 72 km h if the mass of the car is 1500 kg? ›

Work done to increase the velocity of a car from 36 km/h to 72 km/h if the mass of the car is 1500 kg. Hence, the work done to increase the velocity of a car from 36 km/h to 72 km/h, if the mass of the car is 1500 kg is 225000 Joule.

What is the acceleration of a car starting from rest acquires a velocity of 180 meters per second in 0.05 hour? ›

Acceleration, a=180m/s0.05×3600s=1m/s2.

What is the acceleration of a car that increases its velocity from 0 to 100 km h in 10 seconds? ›

Show that the acceleration of a car that can go from rest to 100 km/h in 10 s is 10 km/h s.

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