An object’s position above the ground, s(t), in meters, after t seconds is given by s(t)...

An object’s position above the ground, s(t), in meters, after t seconds is given by s(t) = 16t2+120t+6. (a) What is the position of the object at time t = 3 seconds? (

b) Find the velocity of the object as a function of t.

(c) Find the object’s acceleration at any time t.

(d) When is the velocity of the object 56 m/s?

(e) Find the position of the object at the time when the velocity is 56 m/s. (Hint: Use your answer from part (d).)

Expert Solution

milcah answered 2 years ago

An equation of motion is given, where s is in meters and t in seconds. Find...

An equation of motion is given, where s is in meters and t in seconds. Find (a) the times at which the acceleration is zero, and (b) the velocity at these times. t^4-10t^3+36t^2+2

s(t)= 5t + 3/t^2 be the position in feet of a particle after t seconds for t...

s(t)= 5t + 3/t^2 be the position in feet of a particle after t seconds for t ≥ 1. (a) Compute the average velocity from t = 1 to t = 3. Include units in your answer (b) Where is the velocity = 0? (c) Show the accelaration for t ≥ 1 is positive. (d) What are the units for the acceleration?

Assume that the height of a ball in feet off of the ground after t seconds...

Assume that the height of a ball in feet off of the ground after t seconds is given by the function h(t). If you know the following about the function h and its derivative 1. h(5) = 250 ft 2. h'(1) = 15 ft/sec 3. h'(5) = 0 ft/sec 4. h'(6) = -2 ft/sec Recall that h'(t) is the derivative of h at seconds, and h(t) is the function h evaluated at t seconds. Explain what each of the 4...

The position of a particle moving along a line (measured in meters) is s(t) where t...

The position of a particle moving along a line (measured in meters) is s(t) where t is measured in seconds. Answer all parts, include units in your answers. s(t)=2t^3 +6t^2 −48t+7 −10<t<10 (a) Find the velocity function. (b) Find all times at which the particle is at rest. (c) On what interval is the particle moving to the right? (d) Is the particle slowing down or speeding up at t = −1 seconds?

An object of mass 200kG is at a height of 50 meters above the ground and...

An object of mass 200kG is at a height of 50 meters above the ground and is moving with a speed of 1.8m⁄s . Calculate its: - Potential energy at that height? - Kinetic energy? - Total energy and momentum? - Objects total momentum at that height?

A projectile is fired at a height of 2 meters above the ground with an initial...

A projectile is fired at a height of 2 meters above the ground with an initial velocity of 100 meteres per second at an angle of 35° with the horizontal. Round each result to the nearest tenths of a unit. a) Find the vector-valued function describing the motion b) Find the max height c) How long was the projectile in the air d) Find the range

Suppose P(t) t(3cubed)– 4t + 4 represents the position of a moving particle after t seconds....

Suppose P(t) t(3cubed)– 4t + 4 represents the position of a moving particle after t seconds. a. At what time(s) does the particle change directions? b. When is the speed of the particle decreasing? c. What is the distance traveled by the particle for tE[1, 3]?

For the following exercises, explain the notation in words when the height of a projectile in feet, s, is a function of time t in seconds after launch and is given by the function s(t). s(2)

1. The electric potential two meters above the ground is measured to be -5V. What is...

1. The electric potential two meters above the ground is measured to be -5V. What is the electric field at this point? Select one: a. 2.5 N/C and pointing upward b. 2.5 N/C and pointing downward c. 10 N/C and pointing downward d. You cannot tell from the information given. e. 10 N/C and pointing upward 2. As a charged particle moves a distance of 2 meters, the electric potential increases uniformly by 5V. What is the magnitude of the...

A Ferris wheel is boarding platform is 3 meters above the ground, has a diameter of...

A Ferris wheel is boarding platform is 3 meters above the ground, has a diameter of 76 meters, and rotates once every 7 minutes. How many minutes of the ride are spent higher than 49 meters above the ground?

Question