An electric car is travelling at a speed of 16.0 m/s - Edexcel - GCSE Physics - Question 8 - 2023 - Paper 2

To calculate the time taken for the battery to discharge, we can use the relationship:

$t = \frac{E}{P}$

where:

• E = 126 MJ = 126 \times 10^6 J (total energy transferred)
• P = 17.5 kW = 17500 W (power).

Now substituting the values:

$t = \frac{126 \times 10^6}{17500} \approx 7200 \text{ seconds}$

To convert seconds to hours:

$t = \frac{7200}{3600} = 2 \text{ hours}$

The electrical device serves two functions; during acceleration, it acts as a motor, utilizing battery energy. When the car decelerates, the device functions as a dynamo, converting kinetic energy back into electrical energy to recharge the battery. This process allows for energy recovery, which increases the efficiency of energy usage from the battery, thus extending the time the car can be driven before the battery discharges.

To verify the claim, we can use the formula:

$t = \frac{E}{I \times V}$

Where:

• E = 126 MJ = 126 \times 10^6 J
• I = 15.0 A (current)
• V = 400 V (voltage).

Calculating the time,

$t = \frac{126 \times 10^6}{15.0 \times 400} = 21000 \text{ seconds} = 5.83 \text{ hours}$

Since 5.83 hours is greater than 6 hours, the claim is not justified.

Using the equation:

$E = Q \times V$

Rearranging for charge (Q):

$Q = \frac{E}{V}$

Substituting in the values:

$Q = \frac{126 \times 10^6}{400} = 315000 \text{ C}$

Thus, the total charge that enters the battery is 315,000 coulombs.