how do you change 6t^4 to 24 in instantaneous velocity
Answers
Answer:
ONE OF THE most important applications of calculus is to motion in a straight line, which is called rectilinear motion.
Instantaneous velocity
Consider a particle moving in a straight line from a fixed point O to a given point P, and let t be the time elapsed. Then to each value of t there will correspond a distance s, which will be a function of t:
s = s(t).
When we know s(t), we have what is called the equation of motion.
Now, if the particle moves with constant velocity -- which is called uniform motion -- then we don't need calculus. In other words, if the equation of motion is
s = 22 t,
then at every instant of time, the velocity is 22 m/sec. For, the slope of that line, which is 22, is rate of change of s with respect to t, which by definition is the velocity.
Instantaneous velocity
In each 1 second of time, the particle moves a distance of 22 meters.
Δs
Δt = 22 meters per second.