M1 June 2013 Q5
5. A car is travelling along a straight horizontal road. The car takes 120 s to travel between two sets of traffic lights which are 2145 m apart. The car starts from rest at the first set of traffic lights and moves with constant acceleration for 30 s until its speed is 22 m s\(^{-1}\). The car maintains this speed for \(T\) seconds. The car then moves with constant deceleration, coming to rest at the second set of traffic lights.
A motorcycle leaves the first set of traffic lights 10 s after the car has left the first set of traffic lights. The motorcycle moves from rest with constant acceleration, \(a\) m s\(^{-2}\), and passes the car at the point \(A\) which is 990 m from the first set of traffic lights. When the motorcycle passes the car, the car is moving with speed 22 m s\(^{-1}\).
| Scheme | Marks |
|---|---|
 | Shape B1 Figures B1 |
| (2) |
Notes
First B1 for a trapezium starting at the origin and ending on the \(t\)-axis.
Second B1 for the figures marked (allow missing 0 and a delineator oe for \(T\)) (allow if they have used \(T = 75\) correctly on their graph)
| Scheme | Marks |
|---|---|
| \(\dfrac{(120 + T)22}{2} = 2145\) | M1 A1 |
| \(T = 75\) | A1 |
| (3) |
Notes
First M1 for producing an equation in their \(T\) only by equating the area of the trapezium to 2145, with the correct no. of terms. If using a single trapezium, we need to see evidence of using ½ the sum of the two parallel sides or if using triangle(s), need to see ½ base x height.
Second A1 cao for a correct equation in \(T\) (This is not f.t. on their \(T\))
Third A1 for \(T = 75\).
N.B. Use of a single suvat equation for the whole motion of the car e.g. \(s = t(u + v)/2\) is M0
| Scheme | Marks |
|---|---|
| \(\dfrac{(t + t - 30)22}{2} = 990\) | M1 A1 |
| \(t = 60\) | A1 |
| \(\mathit{Answer} = 60 - 10 = 50\) | A1 |
| (4) |
Notes
First M1 for producing an equation in \(t\) only (they may use \((t - 30)\) oe as their variable) by equating the area of the trapezium to 990, with the correct no. of terms. If using a trapezium, we need to see evidence of using ½ the sum of the two parallel sides or if using triangle(s), need to see ½ base x height.
First A1 for a correct equation.
Second A1 for \(t = 60\) (Allow 30 + 30).
Third A1 for answer of 50.
N.B. Use of a single suvat equation for the whole motion of the car e.g. \(s = t(u + v)/2\) is M0.
Use of the motion of the motorcycle is M0 (insufficient information).
Use of \(v = 22\) for the motorcycle is M0.
| Scheme | Marks |
|---|---|
| \(990 = 0.5a50^2\) | M1 |
| \(a = 0.79\), 0.792, 99/125 oe | A1 |
| (2) | |
| (11 marks) |
Notes
First M1 for an equation in \(a\) only.
First A1 for \(a = 0.79\), 0.792, 99/125 oe
N.B. Use of \(v = 22\) for the motorcycle is M0.