Relationships between Velocity and Acceleration
When v(t)>0 and a(t)>0 the particle in motion is ...
speeding up.
When v(t)<0 is the particle moving to the right or the left ?
The particle is moving to the left.
Steve is growing at a rate of 2 inches/year. What is dh/dt ?
dh/dt = 2 inches/year
Is 0/0 an indeterminate form ?
Yes
When v(t)>0 and a(t)<0 the particle in motion is...
slowing down.
When v(t)>0 is the particle moving to the right or the left ?
The particle is moving to the right.
The radius of a circle is decreasing by 3 inches/hour. What is dr/dt ?
dr/dt = -3 inches/hour
Evaluate the limit as x approaches 2 when x^2-4/x-2.
0.
When v(t)>0 and a(t)=0 the particle in motion is...
maintaining a constant speed.
positive.
If the area of a rectangle is Area=(l)(w) what is dA/dt ? (Use the product rule)
dA/dt = l(dw/dt)+w(dl/dt)
Evaluate the limit as x approaches -2 when 2ln(-1-x)/2x^2-8.
1/4
When v(t)<0 and a(t)<0 the particle in motion is...
speeding up.
When the particle is moving to the left, the velocity of the particle must be...
negative.
If the perimeter of a rectangle is Perimeter=2(l)+2(w) what is dP/dt?
dP/dt=2(dl/dt)+2(dw/dt)
Evaluate the limit as x approaches 0 when x^2-1/x^2+3x-4.
0
Anytime v(t)=0 the particle in motion is...
stopped.
When the speed of a particle is increasing the velocity and speed must both...
have the same sign (+/-).
If the area of a triangle is Area=1/2(a)(b) what is dA/dt?
dA/dt=1/2(a)(db/dt)+1/2(b)(da/dt)
Evaluate the limit as x approaches 0 when 5x-10x^2/ln(2x-1)+x.
5/3