If a car at rest accelerates uniformly to a speed of 144 km/hour in 20 second it covers a distance of

Question

A car starts from rest and accelerates uniformly at 3 m/s\textsuperscript{2. What will be its velocity after 5 seconds?}

Answer 1

To solve this problem, we need to find the distance covered by the car. We are given the initial speed, final speed, and the time duration.

First, let's identify the values given in the problem:
- Initial speed (u): 0 km/h (since the car is at rest)
- Final speed (v): 144 km/h
- Time (t): 20 seconds
Convert the final speed from km/h to m/s: 1 \text{ km/h} = \frac{1000}{3600} \text{ m/s}. Therefore, v = 144 \times \frac{1000}{3600} = 40 \text{ m/s}.
Use the equation of motion: v = u + at to determine the acceleration (a). Substituting the known values, we get: 40 = 0 + a \times 20. Thus, a = \frac{40}{20} = 2 \text{ m/s}^2.
Now, use the formula for the distance covered under uniform acceleration: s = ut + \frac{1}{2} a t^2. Plugging in the known values: s = 0 \times 20 + \frac{1}{2} \times 2 \times (20)^2. Therefore, s = 0 + \frac{1}{2} \times 2 \times 400 = 400 \text{ m}.

Hence, the distance covered by the car is 400 meters. This matches the correct option.

Answer 2

To solve this problem, we need to find the distance covered by the car. We are given the initial speed, final speed, and the time duration.

First, let's identify the values given in the problem:
- Initial speed (u): 0 km/h (since the car is at rest)
- Final speed (v): 144 km/h
- Time (t): 20 seconds
Convert the final speed from km/h to m/s: 1 \text{ km/h} = \frac{1000}{3600} \text{ m/s}. Therefore, v = 144 \times \frac{1000}{3600} = 40 \text{ m/s}.
Use the equation of motion: v = u + at to determine the acceleration (a). Substituting the known values, we get: 40 = 0 + a \times 20. Thus, a = \frac{40}{20} = 2 \text{ m/s}^2.
Now, use the formula for the distance covered under uniform acceleration: s = ut + \frac{1}{2} a t^2. Plugging in the known values: s = 0 \times 20 + \frac{1}{2} \times 2 \times (20)^2. Therefore, s = 0 + \frac{1}{2} \times 2 \times 400 = 400 \text{ m}.

Hence, the distance covered by the car is 400 meters. This matches the correct option.

The Correct Option is A