How to Calculate Initial Velocity of a Moving Object

What is the initial velocity of a moving object if it reaches a velocity of 7.8 m/s over a time of 4.2 s with a displacement of 19 m?

1. 0 m/s

2. 3.5 m/s

3. 5 m/s

Answer:

The initial velocity of the moving object is approximately 0 m/s, indicating that the object started from rest.

To calculate the initial velocity of a moving object that reaches a velocity of 7.8 m/s over a time of 4.2 s with a displacement of 19 m, we can use the equations of motion in physics. The first step is to determine the acceleration of the object using the given data.

We know that displacement (d) is equal to initial velocity (u) multiplied by time (t) plus half of acceleration (a) multiplied by time squared (t^2). This equation can be rearranged to find the acceleration: a = (2*(d - ut))/t^2.

Substitute the values: a = (2*(19 m - 0 m/s * 4.2 s))/(4.2 s)^2, which simplifies to a = 2.15873 m/s^2. Now, we can use this acceleration to find the initial velocity.

By using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can calculate the initial velocity: u = v - at. Substituting the values, u = 7.8 m/s - 2.15873 m/s^2 * 4.2 s, which results in an initial velocity of approximately 0 m/s.

Therefore, the initial velocity of the moving object is 0 m/s, indicating that it started from rest and accelerated to reach a velocity of 7.8 m/s over a time of 4.2 s with a displacement of 19 m.