1 Marking scheme: Worksheet (AS)
1 D
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2 B
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3 C
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4 C
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5 B
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6 a A scalar quantity has only magnitude (size).
b A vector quantity has both magnitude (size) and direction.
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7 Any three sensible suggestions, e.g. distance, speed, volume, area and temperature.
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velocity =
change in displacement
(velocity = rate of change of displacement).
time
b Displacement is a vector quantity and time is a scalar.
Since velocity is determined by dividing a vector by a scalar, it must be a vector quantity.
8 a
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9 speed =
distance
time
600
600
340 =
so t =
t
340
t = 1.76 s ≈ 1.8 s
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10 speed =
distance
time
distance = 0.24 m, time = 4 × 60 = 240 s
0.24
v=
240
v = 0.0010 m s−1 (1.0 × 10−3 m s−1)
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11 a Gradient = velocity
b From the start to 3.2 s: the object travels at a constant velocity.
From 3.2 s to 7.0 s: the object is stationary.
c Velocity at 2.0 s = gradient of line at 2.0 s.
8 .5
∆s
v=
=
∆t
3.2
v = 2.66 m s −1 ≈ 2.7 m s −1
12 a
Distance = 3200 m, time = 15 × 60 = 900 s
3200
average speed =
900
average speed = 3.56 m s −1 ≈ 3.6 m s −1
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b Distance = 3200 + 6200 = 9400 m, time = (15 + 30 + 40) × 60 = 5100 s
9400
average speed =
5100
average speed = 1.84 m s −1 ≈ 1.8 m s −1
AS and A Level Physics
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Original material © Cambridge University Press 2010
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1 Marking scheme: Worksheet (AS)
13 a
Velocity at 4.0 s = gradient of line at 4.0 s
7 .0
velocity =
5. 0
velocity = 1.4 m s–1
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b Velocity at 8.0 s = gradient of line at 8.0 s
7.0
velocity = −
15.0 − 5.0
velocity = –0.7 m s−1 (negative slope, hence the negative sign)
Distance = circumference of circle
distance = 2πr = 2π × 0.70 ≈ 4.40 m
4.40
speed =
≈ 7.1 m s −1
0.62
b i The displacement is the direct distance from point A.
Displacement = 2 × radius = 140 cm (1.4 m)
ii The stone is back where it started, hence the displacement is 0 m.
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14 a
Correct plotting of points.
A smooth curve through all the data points.
b The trolley is accelerating.
The gradient of the graph (which is velocity) increases with time.
c At 0.2 s: velocity u = 0.30 m s−1 (within ± 0.05 m s−1)
At 0.5 s: velocity v = 0.75 m s−1 (within ± 0.07 m s−1)
15 a
v−u
0.75 − 0.30
=
(time taken = 0.5 − 0.2 = 0.3 s)
t
0 .3
a = 1.5 m s−2
d a=
AS and A Level Physics
Original material © Cambridge University Press 2010
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