Answer:
The percentage uncertainty in the average speed is 0.10% (2 sig. fig.)
Explanation:
Consider the formula for average speed
.
,
where
is the total distance, and
is the time taken.
The percentage uncertainty of a fraction is the sum of percentage uncertainties in
- the numerator, and
- the denominator.
What are the percentage uncertainties in
and
in this question?
The unit of the absolute uncertainty in
is meters. Thus, convert the unit of
to meters:
.
.
The unit of the absolute uncertainty in
is seconds. Convert the unit of
to seconds:

Similarly,
.
The average speed
here is a fraction of
and
. Both
and
come with uncertainty. The percentage uncertainty in
will be the sum of percentage uncertainties in
and
. That is:
.
Generally, keep
- two significant figures for percentage uncertainties that are less than 2%, and
- one for those that are greater than 2%.
The percentage uncertainty in
here is less than 2%. Thus, keep two significant figures. However, keep more significant figures than that in calculations to make sure that the final result is accurate.
Answer:
parabolic path
Explanation:
As the cart reaches the end of the table with a horizontally directed velocity (only horizontal component), the cart will follow a parabolic path given by the combined action of:
(1) kinematic equation for motion under constant velocity in the horizontal direction (linear expression in terms of time), and
(2) kinematic equation for motion under constant acceleration (that of gravity) in the vertical direction (quadratic expression in terms of time)
Answer:
9.6 m
Explanation:
This is a case of motion under variable acceleration . So no law of motion formula will be applicable here. We shall have to integrate the given equation .
a = 3.6 t + 5.6
d²x / dt² = 3.6 t + 5.6
Integrating on both sides
dx /dt = 3.6 t² / 2 + 5.6 t + c
where c is a constant.
dx /dt = 1.8 t² + 5.6 t + c
when t = 0 , velocity dx /dt is zero
Putting these values in the equation above
0 = 0 +0 + c
c = 0
dx /dt = 1.8 t² + 5.6 t
Again integrating on both sides
x = 1.8 t³ / 3 + 5.6 x t² /2 + c₁
x = 0.6 t³ + 2.8 t² + c₁
when t =0, x = 0
c₁ = 0
x = 0.6 t³ + 2.8 t²
when t = 1.6
x = .6 x 1.6³ + 2.8 x 1.6²
= 2.4576 + 7.168
= 9.6256
9.6 m
The force exerted on the box is 56 N
Explanation:
The work done by a force on an object is given by

where
F is the magnitude of the force
d is the displacement of the object
is the angle between the direction of the force and of the displacement
For the box in this problem, we have:
W = 2240 J is the work done
d = 40 m is the displacement of the box
Assuming that the force is parallel to the displacement, 
Solving the equation for F, we find the force exerted on the box:

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