Answer:
Halfway between B and A on the return leg.
Explanation:
Your average SPEED for the entire trip will equal your constant speed as the time and distance increase at proportionate rates.
Your average VELOCITY will equal your constant speed while you travel from A to B because time and displacement are increasing at proportionate rates.
When you turn around at B to return, your Displacement is now decreasing while your travel time continues to increase, so your average velocity decreases.
Lets say the distance from A to B is 90 km and your constant speed is 30 km/hr.
your average speed is 30 km/hr because you took 6 hrs to travel 180 km
We want to find your position when your average velocity is 30/3 = 10 km/hr
it took 3 hrs to go 90 km from A to B. Let t be the time lapsed since turn around
your displacement is given by d = 90 - 30(t)
and your total time of travel is t + 3 hrs
v = d/t
10 = (90 - 30t) / (t + 3)
10(t + 3) = (90 - 30t)
10t + 30 = 90 - 30t
40t = 60
t = 1.5 hrs
This will occur when you are halfway between B and A
Answer:
2.28
Explanation:
From mirror formula,
1/f = 1/u+1/v .......... Equation 1
Where f = focal length of the mirror, v = image distance, u = object distance.
Note: The focal length mirror is positive.
make v the subject of the equation,
v = fu/(u-f)............ Equation 2
Given: f = 2.5 cm, u = 1.4 cm
Substitute into equation 2
v = 2.5(1.4)/(1.4-2.5)
v = 3.5/-1.1
v = -3.2 cm.
Note: v is negative because it is a virtual image.
But,
Magnification = image distance/object distance
M = v/u
Where M = magnification.
Given: v = 3.2 cm, u = 1.4 cm
M = 3.2/1.4
M = 2.28.
Thus the magnification of the tooth = 2.28.
Answer:
x(t) = - 6 cos 2t
Explanation:
Force of spring = - kx
k= spring constant
x= distance traveled by compressing
But force = mass × acceleration
==> Force = m × d²x/dt²
===> md²x/dt² = -kx
==> md²x/dt² + kx=0 ------------------------(1)
Now Again, by Hook's law
Force = -kx
==> 960=-k × 400
==> -k =960 /4 =240 N/m
ignoring -ve sign k= 240 N/m
Put given data in eq (1)
We get
60d²x/dt² + 240x=0
==> d²x/dt² + 4x=0
General solution for this differential eq is;
x(t) = A cos 2t + B sin 2t ------------------------(2)
Now initially
position of mass spring
at time = 0 sec
x (0) = 0 m
initial velocity v= = dx/dt= 6m/s
from (2) we have;
dx/dt= -2Asin 2t +2B cost 2t = v(t) --- (3)
put t =0 and dx/dt = v(0) = -6 we get;
-2A sin 2(0)+2Bcos(0) =-6
==> 2B = -6
B= -3
Putting B = 3 in eq (2) and ignoring first term (because it is not possible to find value of A with given initial conditions) - we get
x(t) = - 6 cos 2t
==>
It’s C because just trust
Answer:
The forces that do non-zero work on the block are gravity and normal reaction force
Explanation:
