M Schemes 01
M Schemes 01
M Schemes 01
1 D 2 B 3 C 4 C 5 B 6 a A scalar quantity has only magnitude (size). b A vector quantity has both magnitude (size) and direction. 7 Any three sensible suggestions, e.g. distance, speed, volume, area and temperature. 8 a [1] [1] [1] [1] [1] [1] [1] [3]
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.
velocity =
9 speed =
[1]
[1]
10 speed =
distance time distance = 0.24 m, time = 4 60 = 240 s 0.24 v= 240 v = 0.0010 m s1 (1.0 103 m s1)
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
[1] [1]
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
[1] [1]
13 a
[1] [1]
b Velocity at 8.0 s = gradient of line at 8.0 s 7.0 velocity = 15.0 5.0 velocity = 0.7 m s1 (negative slope, hence the negative sign) 14 a
[1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1]
Distance = circumference of circle distance = 2r = 2 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. 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 s1 (within 0.05 m s1) At 0.5 s: velocity v = 0.75 m s1 (within 0.07 m s1)
d a=
vu 0.75 0.30 = (time taken = 0.5 0.2 = 0.3 s) t 0 .3 a = 1.5 m s2
15 a