Write an equation describing the velocity at any time for an object given an initial velocity of Vo in the positive direction which is acted by an acceleration in the negative direction.
Write an equation describing the position at any time for an object starting from an initial psoition Xo with an initial velocity Vo in the positive direction, which is acted on by an acceleration in the negative direction.
v(t) = Vo + at
where a is negative, in this case.
s(t) = Xo + Vot + 1/2 at^2
where a is negative
If all you wanted was the formulas, why not just look in your text book? They are presented there. I'm sure.
For the equation describing the velocity at any time for an object, given an initial velocity of Vo in the positive direction and acted upon by an acceleration in the negative direction, we use the equation of motion:
v = Vo + at
where:
- v is the velocity at any time,
- Vo is the initial velocity,
- a is the acceleration, and
- t is the time.
In this case, since the acceleration is in the negative direction, we assign a negative value to it. Therefore, the equation becomes:
v = Vo - at
For the equation describing the position at any time for an object starting from an initial position Xo with an initial velocity Vo in the positive direction, and is acted upon by an acceleration in the negative direction, we use another equation of motion:
x = Xo + Vot + (1/2)at^2
where:
- x is the position at any time,
- Xo is the initial position,
- Vo is the initial velocity,
- a is the acceleration, and
- t is the time.
Similar to the velocity equation, since the acceleration is in the negative direction, we assign a negative value to it. The equation becomes:
x = Xo + Vot - (1/2)at^2
Note: The equations provided assume constant acceleration. If the acceleration is not constant, these equations may not accurately describe the object's motion.