Higher November 2017 Paper 2 Q20
20. The velocity-time graph below shows the first 60 seconds of a motorcyclist’s journey.
The motorcycle accelerated from 0 to 12·5 m/s in 60 seconds.
(a) After how many seconds was the velocity of the motorcycle 27 km/h? [4]
(b)
(i) Calculate an estimate for the acceleration at \(t = 30\). [3]
(ii) Tracey argues that this acceleration at \(t = 30\) does not represent the typical acceleration of the motorcycle over the 60-second period.
Explain why Tracey’s argument is correct. [1]
Explain why Tracey’s argument is correct. [1]
(c) Over the same period, the velocity of another motorcycle is given by the equation
\(v = 5 + 0{\cdot}001t^2\).
Find the time for which the velocities of the two motorcycles were the same.
Give this time correct to the nearest second.
You must show all your working. [4]
\(v = 5 + 0{\cdot}001t^2\).
Find the time for which the velocities of the two motorcycles were the same.
Give this time correct to the nearest second.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \((27) \div 60 \div 60\) | M1 | |
| \(\times\ 1000\) | M1 | |
| 7.5 (m/s) | A1 | |
| Reading from graph 40 (seconds) | B1 | FT from ‘their 7.5 m/s’ provided at least M1 previously awarded |
| Scheme | Marks | Comments |
|---|---|---|
| (b)(i) Sight of tangent at \(t = 30\) | S1 | |
| Use of \(\dfrac{\text{difference in vertical}}{\text{difference in horizontal}}\) | M1 | |
| Correct evaluation (m/s2 or ms-2) | A1 | Must be negative |
| (b)(ii) Reasonable statement, e.g. ‘the trend is positive acceleration not negative’, ‘at \(t=30\) it is almost zero acceleration but generally it is positive’ | E1 | Allow FT from (b)(i) being zero, but no FT from (b)(i) being positive |
| Scheme | Marks | Comments |
|---|---|---|
| Attempt to find at least one point, i.e. value of \(v\) for \(0 \lt t \leqslant 60\) | S1 | |
| At least 2 correct plots or 2 appropriate values of \(v\) | P1 | |
| Suitable curve between 20 and 30, or 3 values of \(v\) evaluated in the interval \(20 \leqslant t \leqslant 30\), or 2 values of \(v\) evaluated in the interval \(25 \leqslant t \leqslant 26\) | C1 | |
| 24 to 26 seconds (to the nearest second) | B1 | |
| (12) |
Comments
| \(t\) | (0) | 10 | 20 | 30 | 40 | 50 | 60 |
| \(v\) | (5) | 5.1 | 5.4 | 5.9 | 6.6 | 7.5 | 8.6 |
Note:
| \(t\) (s) | 24 | 25 | 26 |
| \(v\) (m/s) from drawn graph | 5.6 | 5.8 | 6 |
| \(v\) (m/s) calculated from formula | 5.576 | 5.625 | 5.676 |