This 2D motion, called “projectile motion”, consists of a ball projected with an initial velocity in the earth’s gravitational field. The initial velocity vector vo has magnitude vo and direction θo .

Final velocity (v) of an object equals initial velocity (u) of that object plus acceleration (a) of the object times the elapsed time (t) from u to v. Use standard gravity, a = 9.80665 m/s2, for equations involving the Earth’s gravitational force as the acceleration rate of an object.

Initial Velocity is the velocity at time interval t = 0 and it is represented by u. It is the velocity at which the motion starts. They are four initial velocity formulas: (1) If time, acceleration and final velocity are provided, the initial velocity is articulated as.

When you solve projectile motion problems, the kinematic equations have non-zero initial velocities. Well if an object starts from rest then it’s initial velocity would be zero however if it is already in motion then it does have an initial velocity of greater than zero.

Without the effects of air resistance, the speed of an object free falling toward Earth would increase by about 32 ft (9.8 m) per second every second. Terminal velocity is the fastest speed that an object will reach as it falls through the air.

magnitude of Force due to gravity=magnitude of Restoring force, then the acceleration of the body is zero, and the body has maximum constant velocity. magnitude of Force due to gravity < magnitude of Force of the spring, then the velocity of the body decreases until it stops.

At the equilibrium position, the velocity is at its maximum and the acceleration (a) has fallen to zero.

The particle’s maximum speed is 17.3 m/s.

The formula for speed is simply v(0)t. 19.8*15.9= 314.82 m/s for the maximum speed.

Using Calculus Choose a point just to the left of the extremum and another point just to the right. If acceleration is negative to the left and positive to the right, the point is a minimum velocity. If acceleration is positive to the left and negative to the right, the point is a maximum velocity.

The y-values of v(t) represent the velocity (how fast its moving). The particle is considered moving to the right when the velocity function is positive (above the x-axis). The particle is considered moving to the left when the velocity function is negative (below the x-axis).

If 0″>a(t)=p′′(t)>0, the particle is speeding up. If a(t)=p′′(t)<0, the particle is slowing down. If a(t)=p′′(t)=0, then the particle is moving at a constant speed.

Example

1. When velocity is negative, the particle is moving to the left or backwards.
2. When velocity is positive, the particle is moving to the right or forwards.
3. When velocity and acceleration have the same sign, the speed is increasing.
4. When velocity and acceleration have opposite signs, the speed is decreasing.

After 3 seconds, the velocity is 4.5+3×1.5=9 m/s.

Thus the particle changes directions exactly once at t=3 seconds. The acceleration is the first derivative of the velocity. Hence, to get the velocity from the acceleration requires integration in time.