0
Take the derivative of the function.
By plugging a value into the derivative, you can find the instantaneous velocity.
By setting the derivative equal to zero and solving, you can find the maximums and/or minimums.
Example:
Find the instantaneous velocity at x = 3 and find the maximum height.
f(x) = -x2 + 4
f'(x) = -2x
f'(3) = -2*3 = -6
So the instantaneous velocity is -6.
0 = -2x
0 = x
So the maximum height occurs at x = 0
f(0) = -02 + 4 = 4
So the maximum height is 4.
Add your answer:
Earn +20 pts
How can you find the instantaneous acceleration of an object whose curve on the velocity time graph is a straight line?
It is the gradient (slope) of the line.
How do you find height if velocity and mass are given?
1/2mv^2 = mgh
How do you find final velocity given height and mass?
the final velocity assuming that the mass is falling and that air resistance can be ignored but it is acceleration not mass that is important (can be gravity) final velocity is = ( (starting velocity)2 x 2 x acceleration x height )0.5
A stone is projected with a velocity of 58.8 ms at an angle of 30 degree from horizontal find the Time of flight maximum height and horizontal range?
A stone is thrown with an angle of 530 to the horizontal with an initial velocity of 20 m/s, assume g=10 m/s2. Calculate: a) The time it will stay in the air? b) How far will the stone travel before it hits the ground (the range)? c) What will be the maximum height the stone will reach?
How to find the height of the projectile launch if the angle velocity and the distance are given?
Get the value of initial velocity. Get the angle of projection. Break initial velocity into components along x and y axis. Apply the equation of motion .
The velocity of a body thrown vertically upward is reduced into half in one secondwhat is the maximum height attained by it?
The maximum height attained by the body can be calculated using the formula: height = (initial velocity)^2 / (2 * acceleration due to gravity). Since the velocity is reduced to half in one second, we can calculate the initial velocity using the fact that the acceleration due to gravity is -9.81 m/s^2. Then, we can plug this initial velocity into the formula to find the maximum height reached.
Find the instantaneous angular acceleration t5.0 with the instantaneous velocity of 6.0 rads t?
To find the instantaneous angular acceleration, you need to know the time rate of change of the instantaneous angular velocity. Without this information, you cannot calculate the instantaneous angular acceleration at t=5.0s.
1 If you toss a ball upward with a certain velocity it falls freely and reaches a maximum height h What maximum height does the ball reach if you throw it upward with double the initial velocity?
If you throw the ball upward with double the initial velocity, it will reach a maximum height four times greater than the initial height. This is because the maximum height is directly proportional to the square of the initial velocity.
What is instantaneous velocity of a body in terms of its average velocity?
The instantaneous velocity of a body represents its velocity at a particular instant in time, while the average velocity is calculated over a certain time interval. To find the instantaneous velocity from the average velocity, you can take the limit as the time interval approaches zero in the average velocity calculation. Mathematically, this can be represented as the derivative of the position function with respect to time.
What is the instantaneous acceleration a of the particle at t45.0s Hints?
To find the instantaneous acceleration at t = 45.0s, you need to differentiate the velocity function with respect to time. The acceleration at t = 45.0s is the derivative of the velocity function at that time. Apply the derivative to the velocity function to find the acceleration at t = 45.0s.
What is the instantaneous acceleration of the particle at?
To find the instantaneous acceleration of a particle, you would need to know the rate of change of its velocity at that specific moment in time. This can be calculated using calculus by taking the derivative of the velocity function with respect to time. The instantaneous acceleration provides information about how the velocity of the particle is changing at that precise instant.
What is A football kicked off at an angle 20 from the ground reaches a maximum height of 4.7 m What is the initial velocity of the kick?
To find the initial velocity of the kick, you can use the equation for projectile motion. The maximum height reached by the football is related to the initial vertical velocity component. By using trigonometric functions, you can determine the initial vertical velocity component and then calculate the initial velocity of the kick.
How do you find instantaneous velocity from position time graph?
To find instantaneous velocity from a position-time graph, you calculate the slope of the tangent line at a specific point on the graph. The slope represents the rate of change of position at that instant, which is equivalent to the velocity at that particular moment.
Which is the total velocity of a projectile at maximum height?
At the maximum height of projectile motion, the vertical component of velocity is zero while the horizontal component of velocity remains constant. Therefore, the total velocity of the projectile at the maximum height is equal to the magnitude of its horizontal component of velocity.
A ball is thrown from the ground into the air at a height of 9.1 m the velocity is observed to be v7.6i 6.1j in meters per second x axis horizontal y axis vertical and up a to what maximum h?
To find the maximum height, we first need to separate the initial velocity into its x and y components. Since the initial velocity is given as v = 7.6i + 6.1j, the initial vertical velocity is 6.1 m/s. We can use the kinematic equation for vertical motion: v_f^2 = v_i^2 + 2aΔy, where v_f = 0 at the maximum height. Rearranging the equation to solve for the maximum height, h, we have h = (v_i^2)/2g, where g is the acceleration due to gravity (9.81 m/s^2). Plugging in the values, we find h ≈ 1.88 m.
What is A stone is thrown upward with an initial velocity of 6m s What maximum height will the stone reach?
To find the maximum height, we can use the kinematic equation: ( h = \frac{v^2}{2g} ), where ( h ) is the maximum height, ( v ) is the initial velocity (6 m/s in this case), and ( g ) is the acceleration due to gravity (approximately 9.81 m/s(^2)). Plugging in the values, we get ( h = \frac{6^2}{2*9.81} \approx 1.83 ) meters. Therefore, the stone will reach a maximum height of approximately 1.83 meters.
A 0.50kg rock is launched upward with an initial speed of 80.0 meter per second how long will it take for he rock to reach its maximum height?
At the maximum height, the rock's final velocity will be 0 m/s. You can use the kinematic equation v_f = v_i + at to find the time it takes for the rock to reach its maximum height. Rearranging the equation to solve for time t, where a is the acceleration due to gravity, you can find the time it takes for the rock to reach its maximum height.
