OCR MEI M1 2009 January — Question 1 8 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2009
SessionJanuary
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicConstant acceleration (SUVAT)
TypeFind acceleration from distances/times
DifficultyEasy -1.2 This is a straightforward mechanics question requiring only basic calculus (differentiation to find acceleration, integration to find distance) and SUVAT application. All steps are routine: reading initial velocity from the equation, differentiating a linear function, integrating a quadratic, and applying a standard SUVAT equation. No problem-solving insight or challenging manipulation is needed.
Spec3.02a Kinematics language: position, displacement, velocity, acceleration3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae

1 A particle is travelling in a straight line. Its velocity \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at time \(t\) seconds is given by $$v = 6 + 4 t \quad \text { for } 0 \leqslant t \leqslant 5$$
  1. Write down the initial velocity of the particle and find the acceleration for \(0 \leqslant t \leqslant 5\).
  2. Write down the velocity of the particle when \(t = 5\). Find the distance travelled in the first 5 seconds. For \(5 \leqslant t \leqslant 15\), the acceleration of the particle is \(3 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  3. Find the total distance travelled by the particle during the 15 seconds.

1 A particle is travelling in a straight line. Its velocity $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ at time $t$ seconds is given by

$$v = 6 + 4 t \quad \text { for } 0 \leqslant t \leqslant 5$$

(i) Write down the initial velocity of the particle and find the acceleration for $0 \leqslant t \leqslant 5$.\\
(ii) Write down the velocity of the particle when $t = 5$. Find the distance travelled in the first 5 seconds.

For $5 \leqslant t \leqslant 15$, the acceleration of the particle is $3 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(iii) Find the total distance travelled by the particle during the 15 seconds.

\hfill \mbox{\textit{OCR MEI M1 2009 Q1 [8]}}