A car starts with a velocity of 10 m/s and decelerates at 2.5 m/s2. Calculate its velocity, distance, and time to stop.

Initial velocity $u = 10 \, \text{m/s}$.
Acceleration $a = -2.5 \, \text{m/s}^2$ (deceleration).
Time $t = 1.5 \, \text{s}$.
We use the kinematic equation: $v = u + at$.

The velocity after 1.5 seconds is $\boxed{\text{6.25 m/s}}$.

ii) The distance travelled in 1.5 seconds.

Initial velocity $u = 10 \, \text{m/s}$.
Acceleration $a = -2.5 \, \text{m/s}^2$.
Time $t = 1.5 \, \text{s}$.
We use the kinematic equation: $s = ut + \frac{1}{2}at^2$.

The distance travelled in 1.5 seconds is $\boxed{\text{12.19 m}}$.

iii) The time taken by the car to stop.

Initial velocity $u = 10 \, \text{m/s}$.
Final velocity $v = 0 \, \text{m/s}$ (when the car stops).
Acceleration $a = -2.5 \, \text{m/s}^2$.
We use the kinematic equation: $v = u + at$.

The time taken by the car to stop is $\boxed{\text{4 s}}$.

iv) Sketch the velocity-time graph for the motion of the car up to the time the car stopped.

The velocity-time graph will be a straight line.

• The initial velocity at $t=0 \, \text{s}$ is $10 \, \text{m/s}$.
• The final velocity at $t=4 \, \text{s}$ (from part iii) is $0 \, \text{m/s}$.
• The graph starts at $(0, 10)$ and ends at $(4, 0)$.
• The slope of the line represents the acceleration, which is $-2.5 \, \text{m/s}^2$.

v) From the graph determine the distance covered by the car before it stopped.

The graph forms a triangle with the time axis.
Base of the triangle = time taken to stop = $4 \, \text{s}$ (from part iii).
Height of the triangle = initial velocity = $10 \, \text{m/s}$.

The distance covered by the car before it stopped is $\boxed{\text{20 m}}$.

15. a)

i) Determine the acceleration of gravity on the planet.

Length of pendulum $L = 0.5 \, \text{m}$.
Frequency $f = 0.29 \, \text{Hz}$.
The mass of the body ($50 \, \text{g}$) is not needed for this calculation.
The formula for the frequency of a simple pendulum is: $f = \frac{1}{2\pi} \sqrt{\frac{g}{L}}$.

Rounding to two significant figures:

The acceleration of gravity on the planet is $\boxed{\text{1.7 m/s}^2}$.