Instantaneous velocity problems

[Shay10825]

Hi everyone! My calc teacher gave us a huge packet and I need some help understanding some of them. Any help would be greatly appreciated.

2.) Assuming that one story of a building is 10 feet, with what speed, in miles per hour, does an object dropped from the top of a 40-story building hit the ground?
S=s_o+ v_ot - 16t^2
0= 400 + v_oT -16t^2
?now what? I have 2 unknowns

4.) A rock is thrown straight down from a height of 480 feet with an initial velocity of 16 feet per second. (a) How long does it take to hit the ground? (b) With what speed does it hit the ground? (c) How long does it take before the rock is moving at a speed of 112 feet per second? (d) When has the rock traveled a distance of 60 feet?

a.) s=s_o+v_ot-16t^2
s=480 - 16t^2
t=5.47

I can’t get part b, c, and d. How do you find the speed? The equation is for velocity. I know velocity is the magnitude of speed but how do you find it?

5.) An automobile moves along a straight highway, with its position given by
s= (12t^3)-(18t^2)+9t-(3/2)

s is in miles ans t is in hours.

(a) Describe the motion of the car: when it is moving to the right, when to the left, where and when it changes direction. (b) What distance has it traveled in the one hour from t=0 to t=1?

I have no clue.

~Thanks

 

[Tom McCurdy]

Hi everyone! My calc teacher gave us a huge packet and I need some help understanding some of them. Any help would be greatly appreciated.

2.) Assuming that one story of a building is 10 feet, with what speed, in miles per hour, does an object dropped from the top of a 40-story building hit the ground?
S=s_o+ v_ot - 16t^2
0= 400 + v_oT -16t^2
?now what? I have 2 unknowns

4.) A rock is thrown straight down from a height of 480 feet with an initial velocity of 16 feet per second. (a) How long does it take to hit the ground? (b) With what speed does it hit the ground? (c) How long does it take before the rock is moving at a speed of 112 feet per second? (d) When has the rock traveled a distance of 60 feet?

a.) s=s_o+v_ot-16t^2
s=480 - 16t^2
t=5.47

I can’t get part b, c, and d. How do you find the speed? The equation is for velocity. I know velocity is the magnitude of speed but how do you find it?

5.) An automobile moves along a straight highway, with its position given by
s= (12t^3)-(18t^2)+9t-(3/2)

s is in miles ans t is in hours.

(a) Describe the motion of the car: when it is moving to the right, when to the left, where and when it changes direction. (b) What distance has it traveled in the one hour from t=0 to t=1?

I have no clue.

~Thanks

2.) Assuming that one story of a building is 10 feet, with what speed, in miles per hour, does an object dropped from the top of a 40-story building hit the ground?

10*40=400

V=Vo-gt
X=Vot-1/2 gt^2
V^2=Vo^2+2ax

v^2=2*32*400

 

[Tom McCurdy]

4. V=Vo-at
you found t, so plug and chug

 

[Tom McCurdy]

for 4. d you will have 60=1/2 Vot-1/2gt^2
set it equal to zero and solve the quadratic
use the positive time

 

[Tom McCurdy]

For 5, plug it into your graphing calculator the distance from the x-axis should be the distance the car has gone to right right when positive and to the left when negitive.

 

[Shay10825]

But for #4 it wants speed and the equations have velocity not speed.

 

[Gokul43201]

But for #4 it wants speed and the equations have velocity not speed.

What's the difference between speed and velocity ? Make sure you understand this...look at the definitions.

 

[Shay10825]

What's the difference between speed and velocity ? Make sure you understand this...look at the definitions.

Speed is the magnitude of velocity right?

 

[Shay10825]

So would you have to find the vectors to get the magnitude?

 

[Silimay]

On #2, you don't have two unknowns. You know the initial velocity, don't you? Isn't it 0 m/s?

On #4, to get the speed, simply take the absolute value of the velocity (since the rock was thrown straight up, there is no horizontal component of the motion and you don't need to use vectors). For instance, it the velocity of the rock came to be -3 m/2, the rock's speed would simply be 3 m/s.

On #5, try graphing the position graph. (I don't know if you know how to do this or not; a graphing calculator might help.) Then graph the derivative.