Hello, I need some help in Calculus! We are now working on "Position and Velocity"!
One example exercise is: "A toy rocket is fired directly upward with an initial velocity of of 112 ft/sec from a launch pad that is 9 feet high.
First, I have to find out what is the position function and what is the velocity function, well that's not a problem.
Position function: s(t)=16t^2+112+9
Velocity function: v(t)=32t+112
But now, there is a question that asks, "Find the instantaneous velocity at 1.5 second." and later "At what time is the toy rocket at its maximum height?" and last but not least: "What is the maximum height achieved by the toy rocket?
I have no idea how to find that stuff out! Please help me- I actually do not need the answer es just a good and simple explanation!
Thank you very much for a good and helpful respond!
One example exercise is: "A toy rocket is fired directly upward with an initial velocity of of 112 ft/sec from a launch pad that is 9 feet high.
First, I have to find out what is the position function and what is the velocity function, well that's not a problem.
Position function: s(t)=16t^2+112+9
Velocity function: v(t)=32t+112
But now, there is a question that asks, "Find the instantaneous velocity at 1.5 second." and later "At what time is the toy rocket at its maximum height?" and last but not least: "What is the maximum height achieved by the toy rocket?
I have no idea how to find that stuff out! Please help me- I actually do not need the answer es just a good and simple explanation!
Thank you very much for a good and helpful respond!
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I need some help in Calculus! We are now working on "Position and Velocity"!
One example exercise is: "A toy rocket is fired directly upward with an initial velocity of 112 ft/sec from a launch pad that is 9 feet high.
First, I have to find out what the position function is and what is the velocity function, well that's not a problem.
Since the initial velocity is upward, upward motion is positive. As the rocket moves upward, its velocity decreases 32 ft/s each second. The acceleration is in the opposite direction of the initial velocity, so acceleration is negative. Acceleration = -32 ft/s^2
In physics, we use the equation below to determine the velocity at a specific time.
vf = vi + a * t
vf = final velocity = Velocity (t)
vi = initial velocity = +112 ft/s
a = acceleration = -32 ft/s^2
Velocity (t) = 112 + -32 * t = 112 – 32 * t
In physics, we use the equation below to determine the velocity at a specific time.
Position (t) = Initial position + Initial velocity * time + ½ * acceleration * time^2
One example exercise is: "A toy rocket is fired directly upward with an initial velocity of 112 ft/sec from a launch pad that is 9 feet high.
First, I have to find out what the position function is and what is the velocity function, well that's not a problem.
Since the initial velocity is upward, upward motion is positive. As the rocket moves upward, its velocity decreases 32 ft/s each second. The acceleration is in the opposite direction of the initial velocity, so acceleration is negative. Acceleration = -32 ft/s^2
In physics, we use the equation below to determine the velocity at a specific time.
vf = vi + a * t
vf = final velocity = Velocity (t)
vi = initial velocity = +112 ft/s
a = acceleration = -32 ft/s^2
Velocity (t) = 112 + -32 * t = 112 – 32 * t
In physics, we use the equation below to determine the velocity at a specific time.
Position (t) = Initial position + Initial velocity * time + ½ * acceleration * time^2
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