| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with velocity-time graph given |
| Difficulty | Standard +0.3 This is a standard M1 velocity-time graph question requiring straightforward application of SUVAT equations and area-under-graph calculations. While it has three parts and multiple stages of motion, each step follows directly from the previous one using routine mechanics techniques (v = u + at, area = distance). No novel problem-solving insight is required, making it slightly easier than average. |
| Spec | 3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Distance \(= 18t\) | B1 | Lower portion of area |
| Distance \(= (t + [t-5]) \times (30-18)/2\) | B1 | Upper portion of area |
| \(18t + (t + [t-5]) \times (30-18)/2 = 300\) | M1A1 | \(30t - 30 = 300\) |
| \(t = 11\) | A1 |
## Question 4(ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Distance $= 18t$ | B1 | Lower portion of area |
| Distance $= (t + [t-5]) \times (30-18)/2$ | B1 | Upper portion of area |
| $18t + (t + [t-5]) \times (30-18)/2 = 300$ | M1A1 | $30t - 30 = 300$ |
| $t = 11$ | A1 | |
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\includegraphics[max width=\textwidth, alt={}, center]{b7f05d10-9d3c-4098-846d-ca6511c75c5d-3_298_540_262_735}
The diagram shows the $( t , v )$ graph of a car moving along a straight road, where $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ is the velocity of the car at time $t \mathrm {~s}$ after it passes through the point $A$. The car passes through $A$ with velocity $18 \mathrm {~ms} ^ { - 1 }$, and moves with constant acceleration $2.4 \mathrm {~ms} ^ { - 2 }$ until $t = 5$. The car subsequently moves with constant velocity until it is 300 m from $A$. When the car is more than 300 m from $A$, it has constant deceleration $6 \mathrm {~ms} ^ { - 2 }$, until it comes to rest.\\
(i) Find the greatest speed of the car.\\
(ii) Calculate the value of $t$ for the instant when the car begins to decelerate.\\
(iii) Calculate the distance from $A$ of the car when it is at rest.
\hfill \mbox{\textit{OCR M1 2013 Q4 [10]}}