A particle has an initial velocity 3i + 4j and an acceleration of 0.4i + 0.3j. Its speed after 10 s is:?

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Answer

Answer

Answer

Given:
Initial velocity (u) = 3i + 4j
Acceleration (a) = 0.4i + 0.3j
Time (t) = 10 s

Step 1: Find the final velocity (v) using the equation of motion:
v = u + at

Substituting the given values:
v = (3i + 4j) + (0.4i + 0.3j)(10)

Simplifying the equation:
v = 3i + 4j + 4i + 3j
v = 7i + 7j

Therefore, the final velocity is 7i + 7j.

Step 2: Find the speed (|v|) of the particle:
The speed of a particle is the magnitude of its velocity vector.

|v| = √(v_x^2 + v_y^2)

Substituting the values of v_x and v_y:
|v| = √((7)^2 + (7)^2)
|v| = √(49 + 49)
|v| = √98
|v| ≈ 9.90

Therefore, the speed of the particle after 10 seconds is approximately 9.90 units.

Explanation:
- The initial velocity of the particle is given as 3i + 4j, which means it is moving in the positive x and positive y direction. The i and j represent the unit vectors along the x and y axes, respectively.
- The acceleration of the particle is given as 0.4i + 0.3j, which means it is experiencing an acceleration in the positive x and positive y direction.
- Using the equation of motion v = u + at, we can find the final velocity of the particle after 10 seconds. We substitute the given values of u, a, and t into the equation and simplify to get the result.
- The final velocity is found to be 7i + 7j, which means the particle is moving at a speed of 7 units in both the x and y direction.
- To find the speed of the particle, we calculate the magnitude of the final velocity vector using the formula |v| = √(v_x^2 + v_y^2). Substituting the values of v_x and v_y from the final velocity, we simplify the equation to find the speed.
- The speed of the particle is approximately 9.90 units after 10 seconds.

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