Question

A car accelerates uniformly from rest to 20.0 m/s in 5.6 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 9.0 103 N and (b) the weight of the car is 1.4 104 N.

Answer 1

I got;

(a) 32100W (3sf)

(b) 50000W

Step-by-step explanation:

For part (a), we need to calculate the mass of the car first. Here, I assumed you wrote that the weight of the car is 9.0 × 10³N.

So, to calculate the mass, we will use this formula;

W = mg

Where I will use 10N/kg to represent "g".

Substitute the values like so;

9.0 × 10³ = m × 10

(9.0 × 10³)/10 = m

∴ m = 900kg

Now that we have the mass, we can calculate the kinetic energy used by the car when it accelerates and we can use the energy here to calculate power later on! So, the formula will be;

Eₖ = 1/2 × m × v²

Substitute the values;

Eₖ = 1/2 × 900 × 20²

∴ Eₖ = 180000J

Then, we can finally calculate the power used by the car using the formula;

P = E/t

Substitute the values;

P = 180000/5.6

∴ P = 32100W (3sf)

Thus, the average power of the car with the weight of 9.0 × 10³N when it accelerates is 32100W!

For part (b), you just have to repeat the workings from part (a)!

Calculate the mass of the car with the weight of 1.4 × 10⁴N first. Then, you can calculate the energy with the mass you get and finally, with that energy, you are now able to calculate the power!

I hope this helps! Let me know if I have any misconceptions or miscalculations! :)