My last kinematics batch (conceptuals)

1. Aug 30, 2009

clairez93

1. The problem statement, all variables and given/known data

1. Two bodies are falling with negligible air resistance, side by side, above a horizontal plane. If one of the bodies is given an additional horizontal acceleration during its descent, it:
a) strikes the plane at the same time as the other body
b) strikes the plane earlier than the other body
c) has the vertical component of its velocity altered
d) has the vertical component of his acceleration altered
e) follows a straight line path along the resultant vector

2. A bullet shot horizontally from a gun:
a) strikes the ground much later than one dropped vertically from the same point at the same instant
b) never strikes the ground
c) strikes the ground at approximately the same time as one dropped vertically from the same point at the same instant
d) travels in a straight line
e) strikes the ground much sooner than one dropped from the same point at the same instant

3. A particle moves on the x axis.When its acceleration is in the positive x direction and increasing in magnitude:
a) its velocity must be in the positive x direction
b) its velocity must be in the negative x direction
c) it must be slowing down
d) it must be speeding up
e) none of the above must be true

4. The acceleration of an object, starting from rest, is shown in the graph below. Other than at t = 0, when is the velocity of the object equal to zero? (see attachment, disregard writing)
a) during the interval from 1.0 s to 3.0 s
b) at t =3.5 s
c) at t =4.0 s
d) at t=5.0 s
e) at no other time less than or equal to 5 s

Ano bject starts from rest at the origin and moves along the x axis with a constant acceleration of (4m/s^2)i. Its average velocity as it goes from x = 2m to x = 8m is:
a) (1m/s)i
b) (2m/s)i
c) (3m/s)i
d) (5m/s)i
e) (6m/s)i

2. Relevant equations

kinematics

3. The attempt at a solution

1. I'm not quite sure I understand this concept. I thought there was no horizontal acceleration during a projectile's descent?

2. Wouldn't a bullet have more of an initial velocity and thus stay in the air longer perhaps than a ball dropped vertically?

3. If the acceleration is positive, and increasing in magnitude, doesn't this mean that the velocity is increasing at a steady rate? Then wouldn't it be speeding up?

4. Wouldn't the velocity be zero in the interval from 3-4 since the triangles cancel each other out?

5. $$6 = 1/2at^{2} [tex]6 = 1/2(4)t^{2}$$
$$t= 1.73$$
$$[tex]\frac{6}{1.73} = 3.46$$

Not the correct answer. What did I do wrong?

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2. Aug 30, 2009

Staff: Mentor

For a projectile the only force is gravity. This is no longer a free projectile, since something is pushing it sideways. But that doesn't affect its vertical motion.

Only an initial vertical component of velocity will affect the time it takes to fall.

Yes, the velocity is increasing (but not at a steady rate). But not necessarily the speed. It could be moving to the left as it slows down. For example the velocity could change like this: -8, -7, -5, -2, +2, +7.

No. Just because the acceleration is zero in that interval doesn't mean that the velocity is zero.

Find the time it takes to reach x = 2 and the time it takes to reach x = 8. (You found the time it takes to reach x = 6.)

Last edited: Aug 30, 2009
3. Aug 30, 2009

Pengwuino

1. The problem artificially injects a horizontal acceleration. In freefall, there is no horizontal acceleration. In this problem, however, there is, but it isn't due to the gravitational field.

2. No, the vertical component of the velocity acts independently from the horizontal component of a velocity.

3. No, a constant positive acceleration would create a constant positive increase in velocity. If the acceleration is actually increasing, the velocity isn't just increasing, it's increasing at ever more increasing rates!