Standard +0.3 This is a standard M2 power-speed-acceleration problem requiring two simultaneous equations from P=Fv at two different points. The method is routine (F=ma to find driving force, then P=Fv), though the algebra with two unknowns and specific numerical values requires careful execution. Slightly above average due to the simultaneous equation solving, but well within typical M2 scope.
3 A car of mass 1500 kg travels along a straight horizontal road with its engine working at a constant rate of \(P \mathrm {~W}\). There is a constant resistance to motion of \(R \mathrm {~N}\). Points \(A\) and \(B\) are on the road. At point \(A\) the car's speed is \(16 \mathrm {~ms} ^ { - 1 }\) and its acceleration is \(0.3875 \mathrm {~ms} ^ { - 2 }\). At point \(B\) the car's speed is \(25 \mathrm {~ms} ^ { - 1 }\) and its acceleration is \(0.2 \mathrm {~ms} ^ { - 2 }\). Find the values of \(P\) and \(R\).
\(P/16 - R = 1500(0.3875)\) or \(P/25 - R = 1500(0.2)\)
M1
Attempt to use N2L once, can be with \(D\) at this stage
\(P/16 - R = 1500(0.3875)\) and \(P/25 - R = 1500(0.2)\)
A1
Both equations correct, may have consistent wrong sign with \(R\)
M1
Attempt to solve for \(P\) or \(R\)
\(P = 12\,500\)
A1
Allow 12.5 kW
\(R = 200\)
A1
Allow if \(-\)ve, and justified why \(+\)ve (e.g. comment on direction)
## Question 3:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $P/16$ or $P/25$ seen | B1 | Use of Driving force $= P/v$ |
| $P/16 - R = 1500(0.3875)$ or $P/25 - R = 1500(0.2)$ | M1 | Attempt to use N2L once, can be with $D$ at this stage |
| $P/16 - R = 1500(0.3875)$ and $P/25 - R = 1500(0.2)$ | A1 | Both equations correct, may have consistent wrong sign with $R$ |
| | M1 | Attempt to solve for $P$ or $R$ |
| $P = 12\,500$ | A1 | Allow 12.5 kW |
| $R = 200$ | A1 | Allow if $-$ve, and justified why $+$ve (e.g. comment on direction) |
---
3 A car of mass 1500 kg travels along a straight horizontal road with its engine working at a constant rate of $P \mathrm {~W}$. There is a constant resistance to motion of $R \mathrm {~N}$. Points $A$ and $B$ are on the road. At point $A$ the car's speed is $16 \mathrm {~ms} ^ { - 1 }$ and its acceleration is $0.3875 \mathrm {~ms} ^ { - 2 }$. At point $B$ the car's speed is $25 \mathrm {~ms} ^ { - 1 }$ and its acceleration is $0.2 \mathrm {~ms} ^ { - 2 }$. Find the values of $P$ and $R$.
\hfill \mbox{\textit{OCR M2 2015 Q3 [6]}}