Question

A particle moving at a velocity of 7.3 m/s in the positive x direction is given an acceleration of 3.4 m/s² in the positive y direction for 8.5 s. What is the final speed of the particle? Answer in units of m/s.

Answer 1

The final speed of the particle is calculated using the Pythagorean theorem with the initial velocity in the x-direction and the change in velocity obtained from the acceleration in the y-direction over the given time. The final speed is found to be approximately 29.8 m/s.

Step-by-step explanation:

To find the final speed of the particle, we'll need to use the Pythagorean theorem since the particle is undergoing acceleration in the y-direction while moving with an initial velocity in the x-direction. We're given an initial velocity in the x-direction (7.3 m/s) and an acceleration in the y-direction (3.4 m/s²) over a time period of 8.5 seconds.

1. First, calculate the change in velocity in the y-direction using the formula Δv = a × t, where Δv is the change in velocity, a is the acceleration and t is the time. In this case, Δvy = 3.4 m/s² × 8.5 s = 28.9 m/s.
2. Next, we will use the Pythagorean theorem to find the final speed: final speed = √(vx² + vy²). Since the initial velocity in the y-direction is 0 m/s, the final velocity in the y-direction will just be equal to the Δvy we found. Plug the values into the equation: final speed = √(7.3 m/s² + 28.9 m/s²).
3. Thus, final speed = √(53.29 + 835.21) m/s = √(888.5) m/s ≈ 29.8 m/s.

The final speed of the particle is 29.8 m/s.