phys

Suppose the displacement x of another object is related to time t according to x = A sin(2𝜋ft), where A and f are constants. What are the dimensions of A? (Hint: A trigonometric function appearing in an equation must be dimensionless.)

L

Suppose that the displacement x of an object is related to time t according to the expression x = Bt2. What are the dimensions of B?

L/T^2

A juggler throws a bowling pin straight up in the air. After the pin leaves his hand and while it is in the air, which statement is true?

The velocity of the pin is opposite its acceleration on the way up.

A car must always have an acceleration in the same direction as its velocity. It's possible for a slowing car to have a positive acceleration. An object with constant nonzero acceleration can never stop and remain at rest.

false true true

Consider the following equations of motion. v =v0 + atΔx =v0t + 12at2v2 =v02 + 2aΔx (a) Can the equations above be used in a situation where the acceleration varies with time? (b) Can they be used when the acceleration is zero?

no yes

A ball is thrown straight up in the air. For which situations are both the instantaneous velocity and the acceleration zero? (Select all that apply.)

none

A tennis player on serve tosses a ball straight up. While the ball is in free fall, its acceleration does which of the following?

remains constant

An object moves along the x-axis, its position given by y(t) = −3 + 4t. Which of the following cannot be directly obtained from a graph of y vs. t?

the accelaration at any instant

Can the instantaneous velocity of an object at an instant of time ever be greater in magnitude than the average velocity over a time interval containing that instant? can it ever be less

yes yes

Must two quantities have the same dimensions if you are adding them? Must two quantities have the same dimensions if you are multiplying them? Must two quantities have the same dimensions if you are subtracting them? Must two quantities have the same dimensions if you are dividing them? Must two quantities have the same dimensions if you are equating them?

yes no yes no yes