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Solution to Test Paper 2
From Mechanics
Solutions
1 (a)
\displaystyle \begin{align}
& 44 \ \textrm{.}1=\frac{1}{2}\times 9 \textrm{.} 8{{t}^{2}} \\
& t=\sqrt{\frac{44 \textrm{.}1}{4 \textrm{.}9}}=3\text{ s} \\
\end{align}
OR
\displaystyle \begin{align}
& s=\frac{1}{2}\times 9 \textrm{.}8\times {{3}^{2}}=44 \textrm{.}1 \\
& \text{AG} \\
& \therefore \text{Hits ground after 3 seconds} \\
\end{align}
M1
A1
A1
(M1)
(A1)
(A1)
(3 marks)
M1: Use of constant acceleration
equation with \displaystyle v=0
A1: Correct equation
A1: Correct \displaystyle s
1 (b)
\displaystyle \begin{align}
& {{v}^{2}}={{0}^{2}}+2\times 9 \textrm{.}8\times 44 \textrm{.}1 \\
& v=\sqrt{864 \textrm{.}36}=29 \ \textrm{.}4\text{ m}{{\text{s}}^{-1}} \\
\end{align}
OR
\displaystyle \begin{align}
& v=0+9 \textrm{.}8\times 3 \\
& v=29 \textrm{.}4 \text{ m}{{\text{s}}^{-1}} \\
\end{align}
M1
A1
A1
(3 marks)
M1: Use of constant acceleration equation with \displaystyle v=0
A1: Correct equation.
A1: Correct \displaystyle v .
1 (c)
Air resistance would slow the ball down.
B1
(1 mark)
B1: Sensible statement about air resistance.
(7 marks)
2 (a)
B1
(1 mark)
B1: Correct horizontal forces.
Ignore any vertical forces.
2 (b)
\displaystyle P = 900 \text{N}
B1
(1 mark)
B1: Correct value for \displaystyle P .
2 (c)
\displaystyle \begin{align}
& P-900=2000\times 1\textrm{.}2 \\
& P=2400+900=3300 \text{N} \\
\end{align}
M1
A1
A1
(1 mark)
M1: Three term equation of motion
A1: Correct equation
A1: Correct \displaystyle P .
2 (d)
\displaystyle \begin{align}
& 800-900=2000a \\
& a=\frac{-100}{2000}=-0\textrm{.}05 \text{ m}{{\text{s}}^{-2}} \\
\end{align}
Car is slowing down
M1
A1
A1
A1
(4 marks)
M1: Three term equation of motion
A1: Correct equation
A1: Correct \displaystyle a
A1: Correct statement
(9 marks)
3 (a)
\displaystyle R=20\times 9\textrm{.}8=196 N
M1
A1
(2 marks)
M1: Use of \displaystyle R=mg
A1: Correct \displaystyle R .
3 (b)
\displaystyle F=0\textrm{.}4\times 196=78\textrm{.}4 N
M1
A1
(2 Marks)
M1: Use of \displaystyle F=\mu R
A1: Correct \displaystyle F .
3 (c)
\displaystyle \begin{align}
& 100-78 \textrm{.}4=20a \\
& a=\frac{100-78 \textrm{.}4}{20}=1 \textrm{.}08 \text{ m}{{\text{s}}^{-2}} \\
\end{align}
M1
A1
A1
(3 marks)
M1: Three term equation of motion
A1: Correct equation
A1: Correct \displaystyle a .
(8 marks)
4 (a)
3
4
5
4 (b)
2
3
4
5
4 (c)
2
3
4
5
1
2
3
4
5
5 (a)
2
3
4
5
5 (b)
2
3
4
5
5 (c)
2
3
4
5