Question

Автомобіль зі старту розігнався до швидкості 100,44 км/год. Продовжуючи рухатися з тим же прискоренням, він за наступні 4,5 с досяг максимальної швидкості, перевищивши попередню у 2,5 рази. Через який час після старту та на якій відстані автомобіль досяг своєї максимальної швидкості?

Answer 1

Ответ: 7,5с; 261,6м

Объяснение:

Дано:

V1=100,44км/ч=27,9м/с

V2=2,5V1

t=4,5с

---------------

t1-?; S-?

V2=2,5*27,9=69,75м/с

а=(V2-V1)/t=(69,75-27,9)/4,5=9,3м/с²

V2=Vo+at

Vo=0

t=V2/a=69,75/9,3=7,5с

S=Vo*t+at²/2=at²/2=9,3*7,5²/2=261,6м

Answer 2

To solve this problem, we can use the equations of motion. The first step is to find the acceleration of the car. We know that the car accelerated from rest to a speed of 100.44 km/h in an unknown time. Let's assume the time taken to reach this speed is 't1'.

Using the equation of motion:

v = u + at

where: v = final velocity (100.44 km/h) u = initial velocity (0 km/h) a = acceleration t = time taken (t1)

We can rearrange the equation to solve for acceleration:

a = (v - u) / t

Substituting the given values:

a = (100.44 km/h - 0 km/h) / t1

Now, we need to find the time taken to reach the maximum speed. We know that the car continued to accelerate with the same acceleration for 4.5 seconds and reached a speed 2.5 times greater than the initial speed. Let's assume the final speed is 'v2'.

Using the equation of motion:

v2 = u + at

where: v2 = final velocity (2.5 * 100.44 km/h) u = initial velocity (100.44 km/h) a = acceleration t = time taken (4.5 seconds)

We can rearrange the equation to solve for acceleration:

a = (v2 - u) / t

Substituting the given values:

a = (2.5 * 100.44 km/h - 100.44 km/h) / 4.5 s

Now we have the acceleration value. We can use this value to find the time taken to reach the maximum speed.

To find the time taken to reach the maximum speed, we can use the equation of motion:

v = u + at

where: v = final velocity (2.5 * 100.44 km/h) u = initial velocity (100.44 km/h) a = acceleration t = time taken

Rearranging the equation to solve for time:

t = (v - u) / a

Substituting the given values:

t = (2.5 * 100.44 km/h - 100.44 km/h) / a

Now we have the time taken to reach the maximum speed.

To find the distance traveled, we can use the equation of motion:

s = ut + (1/2)at^2

where: s = distance traveled u = initial velocity (0 km/h) t = time taken a = acceleration

Substituting the given values:

s = 0 km/h * t1 + (1/2) * a * t1^2

Now we have the distance traveled.

Let's calculate the values using the given information:

1. Calculate acceleration (a1) to reach the speed of 100.44 km/h: - v1 = 100.44 km/h - u1 = 0 km/h - t1 = unknown

a1 = (v1 - u1) / t1

2. Calculate acceleration (a2) to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - t2 = 4.5 s

a2 = (v2 - u2) / t2

3. Calculate the time taken to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - a2 = calculated in step 2

t2 = (v2 - u2) / a2

4. Calculate the distance traveled: - u1 = 0 km/h - t1 = calculated in step 1 - a1 = calculated in step 1

s = 0 km/h * t1 + (1/2) * a1 * t1^2

Let's calculate the values:

1. Calculate acceleration (a1) to reach the speed of 100.44 km/h: - v1 = 100.44 km/h - u1 = 0 km/h - t1 = unknown

a1 = (100.44 km/h - 0 km/h) / t1

2. Calculate acceleration (a2) to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - t2 = 4.5 s

a2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / 4.5 s

3. Calculate the time taken to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - a2 = calculated in step 2

t2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / a2

4. Calculate the distance traveled: - u1 = 0 km/h - t1 = calculated in step 1 - a1 = calculated in step 1

s = 0 km/h * t1 + (1/2) * a1 * t1^2

Let's calculate the values:

1. Calculate acceleration (a1) to reach the speed of 100.44 km/h: - v1 = 100.44 km/h - u1 = 0 km/h - t1 = unknown

a1 = (100.44 km/h - 0 km/h) / t1

2. Calculate acceleration (a2) to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - t2 = 4.5 s

a2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / 4.5 s

3. Calculate the time taken to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - a2 = calculated in step 2

t2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / a2

4. Calculate the distance traveled: - u1 = 0 km/h - t1 = calculated in step 1 - a1 = calculated in step 1

s = 0 km/h * t1 + (1/2) * a1 * t1^2

Let's calculate the values:

1. Calculate acceleration (a1) to reach the speed of 100.44 km/h: - v1 = 100.44 km/h - u1 = 0 km/h - t1 = unknown

a1 = (100.44 km/h - 0 km/h) / t1

2. Calculate acceleration (a2) to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - t2 = 4.5 s

a2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / 4.5 s

3. Calculate the time taken to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - a2 = calculated in step 2

t2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / a2

4. Calculate the distance traveled: - u1 = 0 km/h - t1 = calculated in step 1 - a1 = calculated in step 1

s = 0 km/h * t1 + (1/2) * a1 * t1^2

Let's calculate the values:

1. Calculate acceleration (a1) to reach the speed of 100.44 km/h: - v1 = 100.44 km/h - u1 = 0 km/h - t1 = unknown

a1 = (100.44 km/h - 0 km/h) / t1

2. Calculate acceleration (a2) to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - t2 = 4.5 s

a2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / 4.5 s

3. Calculate the time taken to reach the maximum speed: - v2 = 2.5 * 100.44 km/h - u2 = 100.44 km/h - a2 = calculated in step 2

t2 = ((2.5 * 100.44 km/h) - 100.44 km/h) / a2

4. Calculate the distance traveled: - u1 = 0 km/h - t1 = calculated in