9 (a) Which of these is a vector? A energy B force C mass D work (b) (i) State the equation that relates acceleration to change in velocity and time taken - Edexcel - GCSE Physics - Question 9 - 2020 - Paper 1

The equation that relates acceleration to change in velocity and time taken is given by:

$a = \frac{\Delta v}{t}$

where $a$ is acceleration, $\Delta v$ is the change in velocity, and $t$ is the time taken.

To calculate the acceleration of the van, we first determine the change in velocity:

$\Delta v = v_f - v_i = 20 \text{ m/s} - 2 \text{ m/s} = 18 \text{ m/s}$

Now we use the equation for acceleration:

$a = \frac{\Delta v}{t} = \frac{18 \text{ m/s}}{12 \text{ s}} = 1.5 \text{ m/s}²$

Thus, the acceleration of the van is $1.5 \, \text{m/s}²$.

To calculate the distance traveled by the cyclist, we can find the area under the velocity-time graph:

1. The area of the triangle can be calculated as:

   $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

2. Here, the base is 15 s and the height is 7 m/s (the final velocity):

   $\text{Area} = \frac{1}{2} \times 15 \text{ s} \times 7 \text{ m/s} = 52.5 \text{ m}$

Thus, the distance the cyclist travels in the 15 s is $52.5 \, \text{m}$.

Factors involving the driver that can affect the stopping distance include:

• Change in Reaction Time: A tired driver or one who is not paying attention may take longer to react to a situation, increasing the stopping distance.
• Effect of Drugs: Drivers under the influence of drugs or alcohol may experience impaired judgment and slower reactions.
• Type of Footwear: Inappropriate footwear (e.g., high heels) may reduce the driver's ability to apply the brakes effectively.
• Driver Behavior: How firmly the driver presses the brake pedal can dramatically affect stopping distance; a stronger application results in shorter distances.

Factors concerning the car or the road affecting stopping distance include:

• Mass/Weight of Car: Heavier cars require a longer stopping distance than lighter ones due to greater inertia.
• Speed of Car: Higher speeds increase the stopping distance as kinetic energy is proportional to the square of speed.
• State of Brakes: Worn brakes may not provide the required stopping force, leading to increased distances.
• State of Tires: Bald or poorly inflated tires reduce traction, increasing stopping distances on wet or slick surfaces.
• State of Road: Conditions such as ice, rain, or gravel can drastically increase stopping distances, requiring careful consideration by the driver.