1. A 0.50 kg cart moves on a
straight horizontal track. The graph of velocity **V _{x} **versus time t for the cart is given below.

(a) Indicate every time t for which the cart is at rest.

(b) Indicate every time interval
for which the speed (magnitude of velocity) of the cart is increasing.

(c) Determine the horizontal position x of the cart at t =
9.0 s if the cart is located at x = 2.0 m at t = 0.

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(d) On the axes below, sketch the acceleration *a* *versus
*time *t* graph for the motion of
the cart from *t* = 0 to *t* = 25 s

*. _{} _{}*

(e) From *t* = 25 s until the cart reaches the end of the track, the cart
continues with constant horizontal velocity. The cart leaves the end of the
track and hits the floor, which is 0.40 m below the track. Neglecting air
resistance, determine each of the following.

i. The
time from when the cart leaves the track until it first hits the floor

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ii. The
horizontal distance from the end of the track to the point at which the cart
first hits the floor

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iii. The
kinetic energy of the cart immediately before it hits the floor

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2. A spring
that can be assumed to be ideal hangs from a stand, as shown.

a. You wish to determine experimentally the
spring constant ** k** of the spring.

i. What
additional, commonly available equipment would you need?

ii. What
measurements would you make?

iii.
How would *k* be determined from these measurements?

3.
A 154 kg bear
runs up a hill that has a slope of 15.0° to the horizontal.
The critter travels 1200 m in 125 seconds. (a) How much work did the bear do on itself? (b)
How much power did the bear develop?

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4. A spring is compressed 3.25
cm by a 105 N force. (a) What is the spring constant? (b) How much potential energy is stored in
the spring?

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5.
One end of a spring is attached to a solid wall while
the other end just reaches to the edge of a horizontal, frictionless tabletop,
which is a distance *h** *above the
floor. A block of mass ** M**
is placed against the end of the spring and pushed toward the wall until the
spring has been compressed a distance

Determine
expressions for the following quantities in terms of ** M**,

a.
The time elapsed
from the instant the block leaves the table to the instant it strikes the
floor.

b. The horizontal component of the velocity of
the block just before it hits the floor

c. The work done on the block by the spring

d. The spring constant

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(b)
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(c)
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(d)
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