A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(a) For the smaller value of $l$, obtain a value for:

(iii) The average value of $t$.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(a) For the smaller value of $l$, obtain a value for:

(iv) The absolute and percentage uncertainty in the value of $t$.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(b) (i) For both values of $l$, calculate the average speed $v$ of the car along the straight section of track using the relationship $v=\frac{s}{t}$.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(b) (ii) Justify the number of significant figures that you have given for your values of $v$.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(c) (i) It is suggested that $s$ is proportional to $l$. Explain whether the readings support this relationship.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(c) (ii) (HARDER) It is suggested that $v^2$ is proportional to $l$. Explain whether the readings support this relationship.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(d) Describe four sources of uncertainty or limitations of the procedure for this experiment.

A student releases a toy car to roll down a ramp, as shown.

The student measures the distance $l$ from the middle of the car as it is released to the bottom of the ramp and the distance $s$ travelled along the straight section before the car stops. He also measures the time $t$ taken to travel the distance $s$. He then repeats the experiment using a different value of $l$.

The student obtained readings with $l=40$ and $60 \mathrm{cm}$, taking each reading for $s$ and $t$ twice. The readings were:

$l=40.0 \mathrm{cm}$ : values for $s$ were $124 \&\hspace{0.17em}130 \mathrm{cm}$; values for $t$ were $4.6 \& 4.8 s$

$l=60.0 \mathrm{cm}:$ values for $s$ were $186 \& 194 \mathrm{cm}$; values for $t$ were $4.9 \& 5.2 s$.

(e) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures.

This apparatus shows a resistor in some water.

A student measures the rise in temperature $\theta$ of the water in $100 \mathrm{s}$ using two different values of voltage.

The student wrote:

'When the voltage was set at $6.0 \mathrm{V}$, the rise in temperature of the water in $100 \mathrm{s}$ was $14.5°\mathrm{C}$. The voltmeter reading decreased by about $0.2 \mathrm{V}$ during the experiment, and so the final voltmeter reading was $5.8 \mathrm{V}$. 'The reading fluctuated from time to time by about $0.2 \mathrm{V}$. The smallest scale division on the thermometer was $1°\mathrm{C}$, but I could read it to $0.5°\mathrm{C}$. I did not have time to repeat the reading.

'When the voltage was set at $12.0 \mathrm{V}$, the rise in temperature in $100 \mathrm{s}$ was $51.0°\mathrm{C}$ and the voltage was almost the same at the end, but fluctuated by about $0.2 \mathrm{V}$ ''

(a) Estimate the percentage uncertainty in the measurement of the first voltage.