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MCA Unified Science: Physics (035) Practice Tests & Test Prep by Exam Edge

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MCA Unified Science Physics Sample Test

1 of 5

Starting from point A, an object moves diagonally 3 meters to the North and 4 meters to the East, before reaching point B. If it took 2 seconds to reach B, what is the magnitude of velocity of the object?

Correct Answer:

2.5 m/s

to solve the question regarding the magnitude of velocity of an object moving from point a to point b, we start by understanding the movement of the object. the object travels 3 meters north and 4 meters east. this movement forms a right triangle where the northward and eastward movements are the legs, and the direct path from a to b is the hypotenuse.

the magnitude of displacement, which is the shortest distance between the starting point and the endpoint, is calculated using the pythagorean theorem. according to this theorem, in a right triangle, the square of the length of the hypotenuse (the longest side of the triangle opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. here, the hypotenuse represents the displacement from a to b.

mathematically, this is expressed as: \[ \text{displacement} = \sqrt{(3\,m)^2 + (4\,m)^2} \] \[ \text{displacement} = \sqrt{9\,m^2 + 16\,m^2} \] \[ \text{displacement} = \sqrt{25\,m^2} \] \[ \text{displacement} = 5\,m \]

the displacement is thus found to be 5 meters. to find the magnitude of the velocity, we use the formula for velocity: \[ \text{velocity} = \frac{\text{displacement}}{\text{time}} \] since the time taken to cover this displacement is 2 seconds, the velocity is: \[ \text{velocity} = \frac{5\,m}{2\,s} = 2.5\,m/s \]

therefore, the magnitude of the velocity of the object as it moves from point a to point b is 2.5 meters per second. this calculation confirms that the correct answer is indeed 2.5 m/s.