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 (a) to change in velocity (Δv) and time taken (t) is given by:

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

where Δv is the change in velocity, calculated as the final velocity minus the initial velocity.

To calculate the acceleration of the van, we can use the formula:

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

Where:

• Initial velocity, $v_i = 2$ m/s
• Final velocity, $v_f = 20$ m/s
• Time, $t = 12$ s

Calculating Δv:

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

Now, substituting into the equation:

$a = \frac{18 \text{ m/s}}{12 \text{ s}} = 1.5 \text{ m/s}^2$.

Therefore, the acceleration of the van is 1.5 m/s².

To calculate the distance traveled by the cyclist, we can find the area under the velocity-time graph. The graph forms a right triangle with:

• Base (time) = 15 s
• Height (velocity) = 7 m/s.

The formula for the area of a triangle is:

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

Calculating the area:

$ext{Area} = \frac{1}{2} \times 15 \text{ s} \times 7 \text{ m/s} = \frac{105}{2} = 52.5 \text{ m}$.

Thus, the distance the cyclist travels in 15 seconds is 52.5 m.

The stopping distance of a car can be significantly affected by several factors involving the driver:

1. Reaction Time: A driver's reaction time (the time taken to respond to a hazard) can vary. A delayed reaction can increase the stopping distance.

2. Tiredness: A tired driver may have slower reflexes, which can also delay their reaction time.

3. Effect of Drugs: Use of drugs (both illegal and certain legal medications) can impair judgment and slow reaction times.

4. Footwear: Inappropriate footwear can impede a driver's ability to operate the pedals effectively, potentially resulting in longer stopping distances.

These factors lead to an increased overall stopping distance due to either increased thinking/braking distance.

The stopping distance of a car is influenced by several factors related to either the car itself or the road conditions:

1. Mass/Weight of the Car: Heavier vehicles require more distance to stop compared to lighter vehicles due to the greater inertia.

2. State of Brakes: Worn or poorly maintained brakes can significantly affect stopping efficiency, increasing stopping distance.

3. Tire Condition: Tires with insufficient tread or improper inflation can reduce grip, meaning the car takes longer to stop.

4. State of the Road: Wet, icy, or poorly maintained roads can create hazardous conditions, increasing stopping distance due to reduced traction.

In summary, both driver behavior and vehicle/road conditions play crucial roles in determining stopping distance.