Past Year Questions Speed-time Graph (Part 2) PDF

# Past Year Questions Speed-time Graph (Part 2) ## Finding the Unknown Values on Axes ### 1. (a) The diagram shows the speed-time graph for part of a journey for two vehicles, a car and a bus. **(i) Calculate the acceleration of the car during the first 18 seconds.** $a = \frac{v - u}{t} = \fra...

# Past Year Questions Speed-time Graph (Part 2) ## Finding the Unknown Values on Axes ### 1. (a) The diagram shows the speed-time graph for part of a journey for two vehicles, a car and a bus. **(i) Calculate the acceleration of the car during the first 18 seconds.** $a = \frac{v - u}{t} = \frac{14 - 0}{18} = 0.778$ m/s$^2$ **(ii) In the first 40 seconds the car travelled 134m more than the bus.** **Calculate the constant speed, v, of the bus.** Distance travelled by the car: $s_c = \frac{1}{2}(18 + 40) \times 14 = 528$m Distance travelled by the bus: $s_b = s_c - 134 = 528 - 134 = 394$m The constant speed of the bus: $v = \frac{s_b}{t} = \frac{394}{40} = 9.85$ m/s ### 1. (b) A train takes 10 minutes 30 seconds to travel 16240m. **Calculate the average speed of the train.** **Give your answer in kilometres per hour.** $s = 16240$m $t = 10 \times 60 + 30 = 630$ s $v = \frac{s}{t} = \frac{16240}{630}$ m/s $v = 25.78$ m/s Converting m/s to km/h: $v = 25.78 \times \frac{18}{5} = 92.8$ km/h ## 2. The diagram shows the speed-time graph for part of the journey of a car. The car starts from rest and accelerates at a uniform rate for 15 seconds before reaching a constant speed of 30 m/s. **(a) Calculate the acceleration for the first 15 seconds.** $a = \frac{v - u}{t} = \frac{30 - 0}{15} = 2$ m/s$^2$ **(b) After T minutes, the total distance travelled is 45 kilometres.** **Find the value of T.** Distance travelled in the first 15 seconds: $s_1 = \frac{1}{2}(0 + 30) \times 15 = 225$m Distance travelled after 15 seconds at constant speed: $s_2 = 30 \times (T \times 60 - 15) = 1800T - 450$ m Total distance travelled: $s_1 + s_2 = 45000$m $225 + 1800T - 450 = 45000$ $1800T = 45000 - 225 + 450$ $T = \frac{45225}{1800} = 25.1$ minutes ## 3. The diagram shows the speed-time graph for the final 40 seconds of a car journey. At the start of the 40 seconds the speed is vm/s. **(a) Find the acceleration of the car during the first 24 seconds.** $a = \frac{v - u}{t} = \frac{v + 10 - v}{24} = \frac{10}{24} = 0.417$ m/s$^2$ **(b) The total distance travelled during the 40 seconds is 1.24 kilometres.** **Find the value of v.** Distance travelled in the first 24 seconds: $s_1 = \frac{1}{2}(v + v + 10)\times24 = 24v + 120$ m Distance travelled in the next 16 seconds: $s_2 = (v + 10) \times 16 = 16v + 160$ m Total distance travelled: $s_1 + s_2 = 1240$m $24v + 120 + 16v + 160 = 1240$ $40v = 1240 - 120 - 160 = 960$ $v = \frac{960}{40} = 24$ m/s ## 4. The diagram shows information about the first 8 seconds of a car journey. The car travels with constant acceleration reaching a speed of vm/s after 6 seconds. The car then travels at a constant speed of vm/s for a further 2 seconds. The car travels a total distance of 150 metres. **Work out the value of v.** Distance travelled in the first 6 seconds: $s_1 = \frac{1}{2}(0 + v) \times 6 = 3v$ m Distance travelled in the next 2 seconds: $s_2 = v \times 2 = 2v$ m Total distance travelled: $s_1 + s_2 = 150$ m $3v + 2v = 150$ $5v = 150$ $v = 30$ m/s