1 Marking scheme: Worksheet (AS) 1 D [1] 2 B [1] 3 C [1] 4 C [1] 5 B [1] 6 a A scalar quantity has only magnitude (size). b A vector quantity has both magnitude (size) and direction. [1] [1] 7 Any three sensible suggestions, e.g. distance, speed, volume, area and temperature. [3] 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 [1] [1] [1] 9 speed = distance time 600 600 340 = so t = t 340 t = 1.76 s ≈ 1.8 s [1] [1] 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) [1] 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] [1] [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 AS and A Level Physics [1] Original material © Cambridge University Press 2010 [1] [1] [1] 1 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 [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 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. [1] [1] [1] 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 [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] [1] 2