A racing car accelerates on a straight road from rest to a speed of 50 m/s in 25 s. Assuming uniform acceleration of the car throughout, the distance covered in this time will bea)625mb)1250mc)2500md)50mCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Given information:

The racing car accelerates from rest to a speed of 50 m/s in 25 s.

Uniform acceleration:

Uniform acceleration means that the car's velocity increases by the same amount in equal intervals of time.

Using the formula:

The formula to calculate the distance covered by an object with uniform acceleration is:
$$s = ut + \frac{1}{2}at^2$$
where:
- $s$ is the distance covered
- $u$ is the initial velocity
- $t$ is the time taken
- $a$ is the acceleration

Calculating the acceleration:

Given that the car starts from rest and reaches a final velocity of 50 m/s, we can calculate the acceleration using the formula:
$$v = u + at$$
where:
- $v$ is the final velocity
- $u$ is the initial velocity
- $a$ is the acceleration
- $t$ is the time taken

Plugging in the values, we get:
$$50 = 0 + a \cdot 25$$
Simplifying the equation, we find:
$$a = 2 \, \text{m/s}^2$$

Calculating the distance:

Now that we have the acceleration, we can substitute the values into the formula to calculate the distance covered by the car:
$$s = ut + \frac{1}{2}at^2$$
Plugging in the values, we get:
$$s = 0 \cdot 25 + \frac{1}{2} \cdot 2 \cdot 25^2$$
Simplifying the equation, we find:
$$s = 0 + \frac{1}{2} \cdot 2 \cdot 625$$
$$s = 625 \, \text{m}$$

Therefore, the distance covered by the racing car in 25 seconds is 625 meters. Hence, option A is the correct answer.

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